I just finished up building a 308 out of an old short action I had laying around. i am getting consistent half inch or less groups. my point is if you take your time and have the right person build it you can have a tack driver from a Remington action. with the 30-06 bold face i know you can use a 25-06 or 6.5-06 and i think a 220 swift. there are most likely more cartridges that will work but i would have to look that up. it all depends on what you want to spend. a good stock and barrel will cost about 300 each and then have someone chamber the barrel. the amount you spend will probably be about the same as a high end bull barrel but you will get better accuracy and have a better quality gun that you would if your just buying one off the shelf.
90% of my guns come from actions with worn out barrels. If you have the action blueprinted and build it right they become excellent shooters and can be built to whatever caliber you wish depending on the action length. With a Rem 700 Long action like you have you can do just about anything you wish from a .338 edge down to .17 Rem. All you need to do is change bolts or have yours opened up. Cheapest is to take the action you have and use a cartridge with the same size diameter as the 06 and build from there. Pacific tool and Die makes bolts with bolt heads that will allow you to change from small .223 case head to Magnum bolt head and allow you to build what you wish.