more like a BONG! sound. lol. that sounds to me like power is getting interrupted to the sound board somehow. the +5 (driving the sound hardware), not the +12 (for the actual amp).
as for "finnicky" voltages, I would be more inclined to say your +5 is set too low. it's enough for the main board, but once it crosses the wiring harness to the sound board, it might be a bit diluted by time it reaches there.
it's relatively easy to check the voltage going to the sound board however, by way of the P1 header on it that the wiring harness plugs into. make note of the numbers on the header, one side will say 1 and the other 9. pin 8 is +5, pin 9 is ground, stick your red meter probe in the +5 side and black probe in the ground, with meter set to 20 VDC range. if it's noticeably low, don't go turning the adjustment knob on the power supply just yet.
like most of these boards now after nearly 20 years of use, the JAMMA edge connectors can get dirty, and the more dirt and gunk that forms on the contacts, the harder it is for the power to efficiently get through. remove the main board and get out one of those pink erasers and vigorously rub at the contacts of the JAMMA edge going up and down on each contact and then going side to side across the whole thing. wipe _all_ the eraser fragments off the board. if you wanna get real intensive with cleaning, 91% isopropyl alcohol and a paper towel has worked fairly effective for me. give it a few to dry (it evaporates fast) then reinstall the board and reconnect the sound board wiring harness, ribbon cable and kick harness and try metering the sound board again.
if all goes to plan, you should see an increase in the voltage. once you're all done testing, leave the probes plugged in and gradually step up the +5 via the power supply's adjustment knob until you get 5.10V at the sound board header. this will allot you plenty of voltage, and it will be within means of safe operation. your power supply will operate more efficiently (the dirty edge connector will result in an increase in current, which can over time damage the connects where power is supplied to the game board) and it should eliminate your BING or BONG problem entirely.
if this somehow doesn't get it, next bet would probably be to reflow the header pins on both the main and sound boards.
EDIT: for reference:
http://arcarc.xmission.com/PDF_Arca...rtal_Kombat_2_Kit_(16-44029-101 Oct 1993).pdf slide over to section 3-2 for the wiring info.