I think it might be what they are doing with the Vpp pin of a 2716. W10 and W11 routes (VMA+Q2) or /(VMA+Q2) to pin21 of the ROM. 2716 datasheet says Vpp = Vcc in read mode but the 2716 jumpers actually have the Vpp pin toggling with (VMA+Q2). This apparently works fine with EPROM types 2716 and 2732. The EEPROM AT28C16 pin 21 is write enable. With this toggling /WE /CE and /OE may end up in a situation the EPROM would go into write mode and corrupt.

from the AT28C16 data sheet
"BYTE WRITE: Writing data into the AT28C16 is similar to
writing into a Static RAM. A low pulse on the WE or CE
input with OE high and CE or WE low (respectively) initiates a byte write"

Try this... Remove both W10 and W11. Find where W10 and W11 jumpers meet at their electrically common leg and jump that to Vcc, +5v.
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They drew P21 as a chip enable so maybe its important for some flavor of masked ROM. Even tho a typical 2716 works in that situation, it is out of what the datasheet says for read mode best I understand. Keeping P21 of an 28C16 at Vcc/Vih/5v should keep it out of write mode no matter what is going on with the other enables.

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I have never tried a test ROM on the WMS sound boards, so not sure about it.

Pin 21 used as a chip enable is not guaranteed to work with every 2716 - these were my findings based on different manufacturer chips:

https://pinside.com/pinball/forum/topic/converting-a-bally-17-to-35-mpu-with-fo597-service-bulletin#post-5271782

The chips I mark as working in that thread for its use case, will actually not work in this situation and vice versa the non-working chips.

All the 2716 datasheets specify pin 21 to be tied high in read mode. The behavior of pulling pin 21 low in read mode is undefined.

Don't know exactly about board version numbers but I know early boards like found in gorgar are missing a few 1uf capacitors found in later boards and I think they fixed a wrong + polarity marker of a 1uf cap near the amplifier. Usually the extra caps are bodged in on the early boards by soldering leads to exposed traces.

Sorry I added text to my last post for clarification. That post I linked required the opposite behavior of 2716 that you need here. So ST brand 2716 chips in your case with pin 21 being used as a chip enable should probably work.

"BUS02+VMA" is an active high signal.
If your sound board has jumper W10 installed meaning the "BUS02+VMA" is connected to pin 21 on the 2716, then you need to use a 2716 that will work (enabled and output data) when pin 21 is high, and not work (disabled and no output) when pin 21 is low. In other words pin 21 behaves as an extra active high Chip Enable.

The other thread requires 2716 that will output data *regardless* of the state of pin 21 and those are what I marked as working - different use case to what you have here. The "non-working" chips in the use case of the other thread behave the way you need here, i.e. only outputs data when pin 21 is high.

W10 vs W11 inverts Q2+VMA active high or active low presumably for some ROM type that may want active high chip select.

I have repaired lots of those square sound boards and never had compatibility problems with any type of EPROM, but I typically used M2716 or whatever the board came in with which MBM2716 i think was popular with WMS. They also used masked ROMs that read back like a 2716 that worked fine in this setup (maybe the reason for this p21 connection).

I am thinking the EEPROM is going to be the problem type because of the nature of the write enable in EEPROM vs Vpp in EPROM. Pulling P21 high by removing both W10 and W11 and jumping to +5v there should allow the AT28C16 to work since P18 and P20 are being controlled.