All right, here are my results (it works!).
I reconfigured the board for 3.3V flash instead of 5V by moving the 0 ohm resistor as described above (well, actually, I lost the resistor so I just used a solder blob). That *has* to be the purpose of those. After removing the resistor, the flash VCC pin was no longer connected to any supply voltage. So yes, at least my board can be configured for a 5V or 3.3V flash chip through those.
I changed out the included AM29F010 chip with an MX29LV040, and checked with the DOS flasher, it was definitely recognized and looks like all address pins are hooked up correctly. The chip I used already had the ROMFILE.1S2 contents flashed to it from my previous experiments. So I stuck it in my G3 Blue and White and it was recognized just like the original SeriTek card is recognized -- good sign!
Finally I shut down, hooked up a SATA drive (contains some Linux partitions) and booted the Mac again. It gave me a warning about the disk not being recognized (obviously, because Macs can't mount Linux partitions). I went into Disk Utility and sure enough, the disk was there! So I installed MacFUSE and fuse-ext2 for Linux disk support, rebooted, and the disk showed up and I can browse the contents! I haven't tested booting from it, but reading from the drive appears to work just fine.
So yes, the cheapo Sil3112 cards (well, the ones I have anyway) are compatible as long as they use a supported flash chip and you make sure they are configured to give 3.3V to the flash chip. Preliminary results look good anyway!