You can rent a Finish Reamer and Go, No-Go gauges from 4-D Reamer Rentals. It's not really that hard:
1. Put the barrel on tight - you will need a barrel wrench for this, so as not to mar the barrel (I use Rosin on the threads);
2. Check the headspace with your gauges in just to be sure;
3. Take a new case, and measure how far the rim is from being flush (I'm assuming you are chambering for .303);
4. Put the barreled action in a vise as Vertical as possible (Lets gravity help you);
5. Use a lot of cutting fluid, put the reamer in the barrel and use a long T handle to reach through the action;
6. Nice you are apprehensive (I don't blame you) turn the reamer 1/2 turn, remove reamer, blow out barrel and reamer with air;
7. Re-Perform until Go Gauge just fits, on a closed bolt;
8. Take your new case, and see if it chambers - I like to feel a LITTLE resistance when I close the bolt.