I believe that either the schrader adapter I'm using is too long or the pin for the presta core isn't long enough for me to be able to use an air compressor. It works fine with a floor pump since a pin doesn't need to be engaged for air to come out. But in my situation of trying to seat a new tire, a pump won't work. I've been searches to see if there are other valve stem adapters that allow this.
You're using the wrong inflator valve on your compressor.
You're likely using this type of inflator valve (aka chuck). It requires the inner pin of the schrader valve of the tire to depress the inner pin of the chuck for the chuck to release air:
Instead you need one of these types of inflator valves which have a manually activated release mechanism (the lever or trigger). The advantage of these types is that they often have a built-in pressure gauge, such as the model on the right. The gauges are not very accurate but are sufficient for eyeballing pressure.
If the valve on your compressor is not replaceable (because it's not your compressor, for example) then you can fill up a portable air tank with the compressor (these tanks have schrader valves) and then hook up your manual-style shrader valve inflator to them. This is also a way to use a tiny little 12VDC electric tire inflator (such as in emergency kits) to build up enough pressure and air reserves to set tubeless tires. It might take an hour to build up 5 gallons at 135psi (and you might burn out a tiny compressor, so you'd take it in chunks) but you'd have enough air to certainly set even a car tire.
Note that this tank has the type of schrader valve outlet that you don't want, but you can easily swap it out.
YOU DO NOT NEED TO PRESS IN THE PRESTA PIN IN ORDER TO INFLATE THE TIRE!! AIR PRESSURE DOES IT, IF THE KNOB HAS BEEN UNSCREWED AND THE PIN PRESSED ONCE WITH YOUR FINGER, TO LOOSEN IT UP.
(Though you do need to somehow get air to come out of the Schrader chuck that's attached to the compressor, and some designs are not convenient in this regard.)
It's possible the Presta/Schrader adapter is too long, I've come across a few steel finished ones a whole mil too long. The brass finished ones have always worked for me, but I'd still compare length if you can get to a bike or auto parts store. Likely easier to buy one than file the adapter you already have or putting something big enough to not damage the Presta head but small enough to not bite the inside of the adapter, like a smooth pebble, or a ball bearing. Just make sure the Presta head is unscrewed enough to not bend the threaded part, and don't put so much pressure as to snap it off in there.
Some gas station compressors need to register air pressure already in the line before it will add pressure to that line. Blowing air into the tube (sounds like you're seating a tubeless tire) likely won't be enough. Once I quickly "filled" my car tire with air to fill the line with pressure, then immediately pushed the chuck onto the totally flat bicycle tube valve.
I think it has been established that the type of chuck you're using, needs the pin of an actual Schrader valve to press the center pin of the chuck for the chuck to release air. If it's not acceptable to replace the chuck, try this - connect the Schrader adapter to a Schrader extender (available in auto parts stores... I recommend the all metal variety) and install this onto the presta valve. The pin in the extender may allow the chuck to release air. Something like these:
Another option is to "help" the tubeless tyre seat by using a cargo strap/motorcycle tiedown/ratchet strop around the rolling circumference of the tyre. Its a farm trick, but works okay on larger bike tyres.
This is a small tractor tyre having the same fix done to seat the bead while inflating.
On a bike tyre you might need to use tape to hold the strap in place - most other vehicles have a flatter profile for the strap to rest on.