I got it to work after lots of trial and error. After talking with Grego2d a bit, I have reason to believe that the darksoft IPS files are not working. He's looking to fix it.
In the meantime, see below what I did to get it working - I walked through all steps in getting the unencrypted file patched for MAME, then got those files working for Darksoft. Special thanks to
@rtw for his Multi Generator to assist.
------------
## How to patch your Street Fighter Alpha 3 ROM
#################
MAME UNENCRYPTED ROM
#################
1 - Obtain the original MAME ROM set for the USA version of Street Fighter Alpha 3 (980904) (sfa3u.zip) and extract it to an empty folder.
2 - Download the decrypted version of SFA3 (980904) from
https://cps2.avalaunch.net/ (sfa3udi.zip) and copy the ROMs contained over the original ROM files.
3 - Delete the files "sz3ud.03c" and "sz3ud.04c" and then rename "sz3udi.03c" to "sz3ud.03c" and rename "sz3udi.04c" to "sz3ud.04c"
4 - Apply the SFA3CE IPS patches from the "graphics" and "unencrypted" folders to the ROMs that match their file names. For Alpha 3 branding, use the IPS files in the "sfa3ce" folder. For Zero 3 branding, use the IPS files in the "sfz3ce" folder.
5 - Zip the contents of your patched folder and rename it to "sfa3ud.zip"
6 - Put it in your MAME ROM directory. You might want to keep a separate installation of MAME for hacks so that they won't contaminate a clean ROM set.
7 - Run the game from the command line in your MAME folder, or create a .bat file in your MAME folder that contains the text "mame64 sfa3ud" and simply run that.
8 - Enjoy!
####################################################
CONVERTING UNENCRYPTED MAME ROM into a DARKSOFT ROM (requires additional fan-made software)
####################################################
1 - Ensure you have followed steps 1-7 of patching your MAME Unencrypted ROM (see above).
2 - Unzip your "sfa3ud.zip" - labeled "sfa3ud" and put it into your MAME ROM Directory.
3 - Add phoenix.key into your "sfa3ud" folder. (Can be found with alternative versions of sfa3ud.zip online).
4 - Add "Qsound_hle.zip" that icludes dl-1425.bin into your MAME ROM Directory. Unzip the file so it is an open folder.
5 - Download the CPS2-Multi ROM generator from author rtw, as posted on Arcade Projects (
https://www.arcade-projects.com/threads/cps2-multi-romset-generator.9425/)
6 - Add the cps262.exe file to the same directory as your MAME binary.
7 - From the MAME binary directory, enter Windows Terminal.
8 - At the Windows Terminal, enter "cps262.exe sfa3ud"
9 - You will see the following compile:
C:\Users\username\Documents\MAME>cps264.exe sfa3ud
sz3ud.03c WRONG CHECKSUMS:
EXPECTED: CRC(6db8add7) SHA1(f6dc8ed330254acab16e42a8e729bca7713c8dc1)
FOUND: CRC(0198ac84) SHA1(8226d7b606f567aea019fa3126a31987b5b774b

sz3ud.04c WRONG CHECKSUMS:
EXPECTED: CRC(d9c65a26) SHA1(8293ef112eaa534b58a3b56721af5d2f53fd1576)
FOUND: CRC(38af80aa) SHA1(4c35616d04ea109d25362dba3e5baa243b7539ad)
sz3.09c WRONG CHECKSUMS:
EXPECTED: CRC(b29e5199) SHA1(c6c215eb5aa37f678a9cafcbd8620969fb5ca12f)
FOUND: CRC(8353dae0) SHA1(b6fd70d95ed5180e4fa953b30f3668b64a24343a)
sz3.13m WRONG CHECKSUMS:
EXPECTED: CRC(0f7a60d9) SHA1(c69e0ee22537312909dacc86d2e4be319d54e426)
FOUND: CRC(d941f463) SHA1(fae09d5d29ef3d9650440e589ac574c98f20b899)
sz3.15m WRONG CHECKSUMS:
EXPECTED: CRC(8e933741) SHA1(f4ac4bfe830dc7df9fe4f680e4e0c053e7cbd8fe)
FOUND: CRC(d25f4fbf) SHA1(dee478f694c11f2ab17821f471ed2ed270d5d113)
sz3.17m WRONG CHECKSUMS:
EXPECTED: CRC(d6e98147) SHA1(37f331fbb1284db446faecade6f484f58c0e1b2a)
FOUND: CRC(5c210d31) SHA1(27e6f75640f1a8b06e23b820fdfcb22728d517cc)
sz3.19m WRONG CHECKSUMS:
EXPECTED: CRC(f31a728a) SHA1(f14136564648f006c1b74afda78349f260524b5f)
FOUND: CRC(a0b6f359) SHA1(4e053f29fda3211d7356d3af8005ad195b199c2f)
WARNING: the machine might not run correctly.
CPS2-Multi ROMset generator (Apr 5 2021/23:11:01) (0230)
coding : rtw
name : sfa3ud
directory: .\cps2\games\sfa3ud\
writing file: flash.01
writing file: flash.02
writing file: flash.03
writing file: flash.04
writing file: flash.05
writing file: flash.07
writing file: flash.09
writing file: flash.11
writing file: flash.06
writing file: flash.08
writing file: flash.10
writing file: flash.12
writing file: key
writing file: name
8 - You should now have a folder in your MAME directory called "cps2" with another folder in it labeled "sfa3ud"
9 - You are now going to copy the NAME file from the sfa3ce-main > ips > darksoft folder and place it in your new "sfa3ud" folder found under "cps2." You will be overwriting over the one that was already there.
10 - Rename the "sfa3ud" to whatever you would like. Copy the directory and all other games to a freshly formatted SD card's /games directory for your darksoft modded CPS2-kit.
11 - Enjoy!