Do the cards misbehave at 12MHz or 8MHz? The first edition of original AT had the ISA bus (still called "AT bus" at that time) running at 6MHz. Memory cards designed for a 6MHz bus are quite likely to misbehave at a "100% overclock" of 12.5MHz. At 8MHz, those cards should all work, given correct configuration. But the performance will be meh, still better than swapping, though.

the seem to misbehave at oth clock rates, but more so at 12.5 MHz

I just ordered new 4 MB SIMMs and will check if they do something

Most 386DX systems with SIMM slots I've seen support 4MB SIMMs.

ok

I'll check

If the cards misbehave at 8MHz, they might have bad memory chips, a bad configuration (base address, memory type, ...) or you need to set a wait state jumper for speeds above 6MHz.

reasonable

I'll check that

two of the cards in fact wouldn't work at all (they're being detected by the BIOS, but as soon as FreeBSD boots, there are bus faults and crashes)

the third one would work but if I put high pressure on the ISA bus (e.g. a bulk transfer over network) it would hang the system

If the card is detected by the BIOS with the correct size, the start address and memory layout configuration is likely correct.

You might want to try a memory test program for MSDOS, e.g. CHECKIT to test the memory on that card.

good idea