You don't need a 32 bit clean ROM for A/UX; A/UX itself doesn't make use of the built-in ROM after it gets past the bootloader, and for the Macintosh OS environment it uses its own modified software ROM that's already 32 bit clean.
A/UX allegedly has other issues with the SE/30. Long and short of it according to the FAQs is 3.0 mostly works but 3.1 breaks some things on older machines. And if you want to use something like a PDS Ethernet card your mileage will definitely vary.
Nothing in that video circuit is going to make it boot. Need to give up in that area.
Time to start looking at ROM/RAM especially if you get no chime and that pattern.
If the battery had leaked in ANY way shape or form in that motherboard, its likely eaten away a via/trace going to the ROM and THAT will stop it from booting. Plus there is a cap that sits right there and leaks, does the same exact thing.
If you get slow chimes, its because RAM addressing lines are broken, or the 74F253 muxes are bad.