I looked around but could not find any practical way to get the BIOSes from my computers into files.
The programs I found were either too complicated (flashrom) or simple (romdumpr.)
The problem with flashrom is that it needs to be aware of the chipset and tries to get that by querying the PCI bus. A 486 computer without PCI will not work.
On the other hand, romdumpr just gets whatever is on the F000:000 segment at the time it runs. This presumes that the BIOS at the top of the 4Gbyte address space has a mirror image at that segment, which is not always correct. Most BIOSes run from the top of the 4Gb address space and then dynamically decompress themselves to RAM memory at F000:0000. (aka shadow ROM.)

Frustrated with this I decided to write my own generic BIOS dumper and the results are attached.
It should work on any computer with at least a 386 processor.
The only limitation is that it does not auto detect the BIOS size, which needs to be provided.
(Testing / comments are welcome.)
It runs on DOS (any version above 3) but should also work in FreeDOS (not tested,) in which case it can be placed on a Rufus formatted bootable memory stick and ran from there.