I am curious to find out if anyone has figured out a viable solution for a 1x9 wide range eg; 11 to 46 or 11 to 50 setup without using a derailleur hanger extension? I have a FS mtb and am not too concerned with large steps between gears. It's currently a 9 speed hg401 11 - 36 with a Shimano RD-M370 long cage and with the B screw all the way out I have a solid 10mm between the RD pulley and cassette in 1st gear. I don't want to go with more speeds unless there's a less expensive solution than replacing only the cassette and possibly rear derailleur. I can't find a 10, 11, or 12 speed groupset for less than $150ish and that's a cheap setup.
The Microshift Advent is a 9 speed derailleur that they say is rated to a max cog size of 42-46, with a capacity of 47, so it should be fine for an 11-46 setup. Only compatible with their shifter according to them, so it might not come in under your budget if you include the cost of cassette, derailleur, and shifter, but it's preobably pretty close.
Sun Race makes a wide range 9-speed cassette the CSM980 which is an 11-40T. That's pretty good range and the cassette is quite inexpensive (looks like aprox $35 USD after a quick google). If you need a bit more space you can get a longer b-screw.
Next cheapest option would be grabbing an inexpensive wide range 10-speed cassette (Sun Race being the usual option) and an old long cage 10-speed Shimano derailleur and shifter (and 10-speed chain obviously). Depending on where you source parts this could be fairly inexpensive. You may need a longer b-screw. There are lots of guides on old forums on doing wide 1x10 setups (that was quite popular before 11 and 12 speed became accessible).
More expensive but an amazing deal would be a brand new Shimano M4100 group. It can be found overseas for around $100 USD with derailleur, shifter, cassette and chain. The cassette options are 11-46T or 11-42T. The derailleur may have the serial scratched out (as is often the case with bulk oem parts being sold likely against their contract). I think retail pricing is over 2x that price.
Well, I have it working fairly well. In hindsight I wish I would have gone with the complete Microshift Advent setup but that's how it goes for me being a stubborn miser. I got a Sunrace 11 to 46t 9 speed cassette. My existing rear derailleur works but I did have to use a hanger extender. I also had to get and modify a steel hanger because the aluminum one just couldn't take the load of the shifting with the additional length.
I had to remove some material from the steel hanger to make it fit the dropout and it still sits at a different angle which puts the derailleur mount a little further toward the rear of the bike and I think a little higher as well but with the b-screw all the way in I have just enough clearance so that it doesn't crash in the lower gears. I may remove a little more from the hanger next time I have it apart back there or if it starts crashing with use/wear so that it puts the mount hole closer to where it should be.
But if I don't have any issues I may just leave it where it is because of the last section of the cable. In order for the cable to not seem like it wants to kink where it goes into the barrel adjuster I had to use a longer than usual section of housing back there to provide adequate travel of the rear derailleur with the longer travel from the wide range cassette. With the derailleur positioned further back and upright it eases this condition and allowed me to shorten up that last piece of cable so that it's tighter to the frame and less likely to get caught on things out in the wild.