You are correct about the 49-way control, and yes it can be replicated.
I'm currently using MAME-2003 and a PS4 controller. The left analog stick absolutely works well with Sinistar. When playing, gradually rotate the stick and you will see it handles more than 8-way control.

FWIW: I couldn't get the same results with MAME-2003-Plus. I think it has special configurations to handle analog, but I never researched, as 2003 (standard) does the job well.

@edmaul69 Ugh, sorry about the typos. Power supply is definitely 5v 2.5a (included in my RP kit) I also tried another 5v 5a supply, and the USB connection on the breakout box which is 5v 1a and actually works fine (though I use the kit supply in the permanent installation).

If anything downstream of the PI is PCM rather than Bitstream, it causes problems, so if anyone finds this in a search, make sure that your TV and audio system are all set to Bitstream.