Mike, I may be headed down a rabbit hole with this story, but I too had sound issues on the H8. In my case, the tone was more of a squawk than a beep, and I eventually tracked it down to
IC103 on the
front panel board. I hit the socket with DeOxit and reseated the chip which fixed my issue. I don't think you have the same issue, but I learned some things about how tones are generated via front panel IC103. That IC is a 14040 12-bit counter that is used to create a couple of different tones for the sound circuit based off the system clock. One of the interesting things is that sound circuitry also generates a beep when a
system reset is detected on
IC103, pin 11 (the 14040). It sounds like you have two different devices/cards that are triggering a reset on system boot.
I wonder if this would happen if both H8-1 cards are configured for the same memory address block, or one is jumpered for the 0K block? You have probably checked that already, but if not there are jumper links in the upper right side of the H8-1 card. If the two H8-1 memory cards are the only ones in the system, I think a proper configuration would be to set one with the 8K jumper in place, and the other with the 16K jumper in place.
None of this may apply to your issue, but hopefully is helpful,
Tim