This won't necessarily help the OP, but it may help other riders in a similar situation.
Stack and reach defined
First, let's review what stack and reach are. Stack and reach are usually measured to the top of the bike's head tube. Here's an article by Road.cc, and a picture from their article.
Basically, reach is how long the bike is (i.e. the horizontal measurement). Stack is how tall it is. Stack and reach are usually measured to the top of the head tube (as in the graphic above). Your handlebar position further modifies how the front end of the bike feels. You can add several spacers under the stem. You can change the stem length. You can also get handlebars with less or greater reach and drop.
It sounds like the OP thinks he has short legs relative to his height. This should mean that he wants to look for bikes that have relatively low stack, and relatively long reach.
How would you use stack and reach to shop for bikes?
Bike Insights is a database of frames. They plotted the stack and reach of various frames, and they estimated the average stack/reach ratio as a function of frame size (possibly through regression). They characterize a bike's fit as aggressive (compared to others in its category) if it's longer and lower (i.e. higher reach, lower stack) than average, or upright if it's the reverse. For example, the 2014 Fuji Track Classic appears to have relatively aggressive fit. The gray diagonal line is the stack/reach trend of the average track bike. The colored dots are the stack/reach measures for each size of the Fuji frame I mentioned.
The 2006 Rivendell Quickbeam is very much the reverse.
So, the OP should probably find frames with relatively aggressive fit (if I understood the post correctly). He could find the stack and reach of his current frame, and possibly estimate his desired stack and reach. Naturally, he could ask around at local bike stores; the more experienced sales people should have a sense of which brands they carry are more aggressive or more upright in fit. If the OP uses Bike Insight, their search function appears to allow you to search for a maximum and minimum stack and reach, so the OP could search this way if he can estimate a desired stack and reach. He could also ask a bike store for recommendations, e.g. "I ride about a 52cm frame, and I'm looking for a new track frame with relatively aggressive fit." Bike stores would probably understand nominal sizing more than raw stack and reach numbers, although they will be able to look up stack and reach.
The main limitation of Bike Insight is that the frames in the database are limited to what the site owners have been able to mine from public data, or to what interested users have entered. Thus, this isn't a complete database, and it doesn't have many track frames in it. Also, stack and reach may not be provided by all manufacturers, and older frames in particular may lack these measures. They can be estimated from other measurements, but not all manufacturers may provide the necessary detail. This doesn't affect more current frames as badly.
The limitation of bike stores is that you're limited to the brands they carry, and the sales staff may not be familiar with all the brands they carry. In the US, Trek and Specialized seem to be encouraging retailers to mostly carry their own bikes. Where I live, one chain is mainly a Trek dealer, and it has only a few other brands (mainly ones affiliated with Quality Bicycle Parts, e.g. Salsa). Another chain is mainly a Specialized dealer, and it also carries a few QBP brands, but no others. This may limit shoppers' choice.
Bike Insight doesn't appear to have nominal size as a search parameter, so it isn't possible to tell the site to, for example, "find 52cm bikes with aggressive fit." Many bikes are sized categorically, e.g. S, M, L, XL, possibly with XS and/or XXL, so the number of size categories varies. Some frames are still sized in centimeters, like the two example frames I gave, but this frame size can be arbitrary as discussed below. Thus, nominal size may not be conducive to being used as a search parameter on Bike Insight. I'd still recommend knowing your approximate frame size if you shop at a store; for this purpose, I would estimate a size based on a virtual top tube measurement (i.e. the length of the top tube as if it were level; in the first picture, extend the reach measurement backwards until it intersects the center of the seatpost).
In a more general case, someone with proportionately short or long legs could use the same information. If one is shopping for road bikes, then the average performance road bike (i.e. a road bike designed mainly for racing, e.g. the Trek Emonda or Madone) should have shorter stack and longer reach than an endurance road frame of the same size (i.e. a road bike designed more for long enjoyable rides, e.g. the Trek Domane). Shoppers might want to take this into account. Naturally, bikes will vary within the category as well, e.g. within performance road bikes, Specialized frames appear to have relatively aggressive fit, whereas Trek frames appear to be about average.
Also, some riders may be sensitive to the bike's seat tube angle, which affects how far forward or aft you can position the saddle. I believe most people are not in this situation, but it is worth noting. (I prefer a very forward saddle position, and I can't achieve this on bikes with less than a 74 degree seat angle, which does rule out a few gravel bikes in my size.)
For an example of nominal frame sizing, the Specialized Roubaix is a performance road bike. It's available in 44cm, 49, 52, 54, 56, 58, and 61cm sizes. In the past, road bikes were often made 'square', i.e. a 50cm seat tube and 50cm top tube, and the I believe the nominal sizes would correspond to the ST and TT measures. In the Roubaix, each size's virtual top tube measurements are usually longer (sometimes much longer) than the frame's nominal size. They are compact frames, so the seat tube measurements are all smaller than the nominal frame size.
Compact frame design and miscellaneous thoughts
Speaking of compact frames, i.e. frames with sloped top tubes, my recollection was that this design started in mountain bikes. Giant Bicycles may have been one of the first manufacturers to offer compact road bike frames. The design has become commonplace. This SE post discusses compact frames and their pros and cons.
I recall that one of the advantages is that with a compact frame, a frame with a fixed reach may be able to fit more riders. Riders vary in their leg length, after all. If you only have access to frames with level top tubes, then a rider with short legs will be limited in their frame choice by their standover clearance. A compact frame can give them more standover clearance for the same reach.
I do not believe that compact frames have inherently shorter reach than traditional frames. The OP may be confused about compact geometry. This may stem from a language barrier and unfamiliarity with this terminology, and the OP hasn't clarified. In any case, I'd focus on the stack and reach of the frame, rather than the nominal size. If the frame's reach is correct but you have a lot of standover clearance, I don't believe this is abnormal. Most bikes come equipped with 350mm seatposts as standard, and it appears pretty common to have a lot of seatpost exposed. However, if the OP really has short legs, then he will have relatively little exposed post.
(A personal note: I am 5'5", or 165cm tall. I have relatively short legs. I have about 7cm of exposed seatpost on both my bikes. My gravel bike came stock with a 350mm seatpost, so the vast majority of the post is well inside the frame.)
In general, many professional road cyclists are known to take relatively small frames and use very long stems. Their positions are very, very much lower than the average cyclist, so they may need to do this to achieve a low enough position. In any case, this demonstrates that it is OK to buy a relatively small frame and use a long (within reason) stem and seatpost. (As a personal example, most bikes in my size come stock with a 100mm stem, but I need a 120mm stem on my gravel bike.) This by itself should not disqualify a frame. Some riders may want to consider toe overlap: if you turn the wheel at very low speed, your toe can contact the front wheel if it is too close to your foot. If you are riding a small frame, this can be worth considering. I think that taller riders don't typically experience toe overlap, however. In addition, toe overlap doesn't affect you when riding at speed - you lean the bike to turn, and you usually won't lean it far enough to contact your toe. It can be an annoyance when starting from a stop, but I believe most cyclists can learn to deal with it.
The one time I've ever crashed from toe overlap happened in the sand pit in a cyclocross race. I was not very experienced, and my front wheel was wandering back and forth a bit. Unfortunately, I happened to jerk the wheel just at the time when one of my feet was at the 9 o'clock pedal position, and I went down. This was a mild mishap, considering that it happened at very low speed and on a soft surface. I relay this to illustrate how atypical it is for toe overlap to bring someone down on a road bike.
