Is it possible to make a copy of the GDROM until an original GDROM turns up?
no, retail GD-ROMs can not be copied
I think it needs to be updated in stages for anything below 3.03. I think version 2.13 needs to go to 3.17 before 4.02 or it could get bricked.
That might be the secret... And why we hear stories of conflicts.
2.xx (or lower) you MUST go 3.17 first, 3.xx you may go directly to 4.01/4.02...
things got weird and confusing here. afair this information came from person who did original 1.0x DIMMs upgrade, via desoldering and flashing BIOS chip, but I think it was just coincidence and something else went wrong (i.e. bad soldering, solder bridge, etc), because number of other people did direct update from 1.0x or 2.x to 4.01/4.02 and it worked just fine.
in any way, that origin story was NOT about Net-DIMM update but original DIMM, so, there no need to go to 3.17 first.
Is it any game GD that also updates the DIMM firmware version?
yes and no.
Firmware Update discs came with VF4 game (3 known different revisions came with 3 different VF4 versions). but no, there is no game which may update DIMM on its own.
add: strictly speaking, there is "Dragon Treasure" medal / coin pusher games series, where game disc include DIMM firmware update.