If you strip the receiver of all parts and furniture (including the lower tang) you should be able to get the reamer to turn by hand using an extension tap handle. I point the muzzle down, clamp the barrel (properly padded) in a vise, brush cutting oil on the reamer, insert and start counting quarter- or half-turns. At, say, 10, I pull the reamer out, brush off chips, run a patch down the barrel (put a trash bag under it to catch the debris), inspect, re-oil and start again. With a dummy cartridge you can relate the number of partial turns to your progress down the barrel. Every once in a while, when you've swabbed out the barrel, loosen the vise and turn the octagon barrel halfway around, or 1/4th the way around. That way, your hand pressure doesn't have a chance to skew the reamer seriously. (Since the chamber is already mostly established, it would be rather hard to run it out badly anyway, without a lot of effort and concentration, especially if you rent a good reamer with a proper pilot.)
It is rather tedious, and a little scary, the first time you do it. But you'd be surprised how well these things usually turn out. The Olde-Tyme Gunsmythe's Secret is to pay attention to what you're doing and go slow, checking your progress often. If it takes all evening and an hour or two the next morning before your reamer is to the level of your old rim seat, that will be, what, two shooting sessions worth of time? You'll find yourself shooting your "new" rifle a lot more than the "store-boughten" ones, just because you put your own effort into it.