Looks like you're sorted.
Sometimes reseating the wheel in the dropout can change the position of the rim a couple of mm, and that can sort out a rubbing brake. This is as simple as loosening the quick release, giving the wheel a wiggle, then properly tightening the QR.
You're right that it's unusual to find a v brake with no balance adjustment screw. Some models have the adjuster just one side, which is all that's needed for balancing the brake. Though it's usually a Philips head screw, some brakes use a small allen head grub screw which can be difficult to see. I'd want to upgrade a brake with no adjuster screw.
Shimano Deore (and better) work nicely and are easy to set up, and they're available at reasonable prices now that almost everyone wants disc brakes.