Do you have the jackplate in hand? I wouldn't do it until you have it.
I'd do similar, first I expand the hole 4 ways, then between those spots to 8 ways, etc. Get it just undersize. Once you round it out, keep it round. Keep holding up the jackplate for comparison, make sure you're not too big. Looks like there's a little forgiveness with the lip of the plate, plus you say it's a cheap backup bass so if there's a little gap not a big deal. But you should be able to get it just right if you keep trying the jackplate constantly. When it just starts to go, you'll feel where you need to whittle the wall of the hole just a tad more.
If it was me, I'd clamp down the bass securely, and be using a 1/2" die grinder bit in a drill to make my work faster and easier, just keep going around and around, in and out, keeping it round and on center with the body. By the time I get close, I'll be comfortable with just a light touch to finish the hole. Or finish it by hand.