CLP is not really that useful in getting an old milsurp bore clean. There are non-toxic foaming bore cleaners that will do a much better job. They take a while and I've found that multiple cycles are often necessary, but they do work.
Your rifle is one of the Golden State / Sante Fe sporterized milsurps. The heyday was the '50s and '60s. They are good, solid rifles.
The Mauser sporters were built on surplus military '98s or (later) Spanish Santa Barbara commercial actions. If there is no thumb notch in the left side receiver wall (just in front of the bridge), you most likely have a Santa Barbara that was originally made for the .30-06. These rifles were barreled with mid-grade barrels that realistically are good for 2-3 MOA. That was considered perfectly adequate, even good, back in the day: we're spoiled now. A nice Mauser-actioned sporter in .30-06 that will shoot into 2-3 MOA is a very good rifle.
As to the boltface diameter, it's the same across a surprisingly wide swath of cartridges, from .243 Win thru .250 Savage, 7x57, .308, 8x57, .30-06, .35 Whelen, even .45ACP! There are probably a couple dozen factory cartridges that share the same .473 diameter, to say nothing of wildcats.
Since you have a long action, however, rebarreling to a short action cartridge like the .308 will require extra work to ensure feed reliability. If you do end up needing to rebarrel (not likely), I'd keep the .30-06 chambering. It's the most versatile rifle cartridge ever developed.
Don't give up on reloading. Setting up to load for this rifle is simplicity itself: a LEE hand press kit to neck-size the brass, LEE dies, some powder scoops, powder, primers, and bullets, done. Fits in an ammo can, costs well under $150.