Being as A600 motherboards are a lot cheaper to replace than the A630, and indeed some A600 accelerators, like the A1200 ones, do have issues with certain motherboards, I would be inclined to replace that first.
In the UK Amiga Retro Experience always sells boards, see:
eBay Linkbut I understand NTSC A600s are a little rarer. Even if you have to buy the whole A600 to try it, the results of having a cute 030 powered machine are great see my old A600
here. If you have to get a grubby A600 cheap, then at least you can put the motherboard inside your existing case and you have a spare internal FDD and keyboard. I will put 10 dollars on the motherboard being the problem.