I've used a system 6 board in a system 4 + 3 board without issue in the past.

The one thing that might be an issue is if it has the 8T28 data line tranceivers removed, and you're using the original masked roms (not 2716s)

Or maybe your memory protect signal from the cab is bad?

Verify the original roms to make sure they're still good. Burn a new set to make sure. If your system 6 boards don't have the buffers like zacaj says, they won't work with masked roms. From a software standpoint there's no difference between system 4 and 6 regarding getting them to run on either board. (system 4 software works in system 6.... system 6 software works in system 4 except for firepower).

This may be a bit rusty but...

System 6 added a memory protect signal. Basically the R/W pin of the 5101 ram can't go into 'write' mode for portions of the ram unless the coin door is open, to prevent bugs/etc from messing with the adjustments. So if that signal was messed up (either on the board or coming into J4 from the cab), it's possible that could mess with a system 6 board booting, while on a system 4 board that pin is N/C. Not the first place I'd look though, but just one of the few differences between system 4 and 6 that I could think of

burn new 2716 roms for it. you can swap faulty roms all you like they wont start working

Most it would do is put you into audit mode, which I consider a success since it means the board is at least booting. J4 shouldn't have anything on the memory protect line since it wasn't installed on those games.

I think the OP should get some test roms going first before delving farther. Leons' and pincoders although if Leons' works I've never had an issue just popping game roms in there, but I also have a stack of boards that are in the "maybe they work maybe they don't" status.

I've seen a lot of times where leons would work but then bad ram, bad sockets, memory protect, etc would still prevent the main rom from actually booting

Does the original sys 6 board have original sys 4 PROM/ROMs? If so, check the jumpers on the sys 6 board from the game. You need to change them from the default of a typical sys 6 game to use the ROMs from a sys 4 board.

When IC14 game ROM is used in place of PROMs, Jumper J3 must be connected and J4 removed (IC14 address 600016). When IC14 game ROM and PROMs are used Jumper J4 must be connected and J3 removed (IC14 address 680016).

I’ve ran system 6 boards in my Stellar Wars when I had it.
All good info posted so far. Follow what they are saying. Should work.?

I'm probably insulated from that because I replace the sockets or use the Seigecraft 2764 adapter, and I always install NVram.