Are the original bearings noisy?
If they're not noisy, I'd try adjusting them up, and then test it again. Even if you just tighten the one ring to remove play, it'll give you a far better idea of what condition the spindle is in.

As for potential replacements, it'll depend on the space available. Do you have any photos of the existing head?
Personally, I'd be looking at something that makes tool changes reasonably easy, like a BT spindle, so you can swap tools without having to worry about setting tool lengths.