I suggest you be very reluctant to disassemble (or hire someone to disassemble) your rifle until you have tried everything else to resolve the problem.
IMHE,The BLR is not a Winchester or Ruger that can be rebuilt using a nail and a rock, they only go back together one way and there are many reports of people being unable to re-time them easily or quickly. You may end up with a box of parts or a big invoice for gunsmith’s time. Make sure your gunsmith has done this many times before and knows how to do it properly. I have completely stripped and assembled every other firearm I own, but my BLR has never been disassembled in the 40 years that I have owned it.
You do not say what year your BLR is or where it was made. My pre 81 308W BLR has a very small chamber, and I used SB (small base) dies for many years as rounds would not chamber smoothly if loaded with standard dies. My gunsmith told me this was quite common in lever and semi-autos as they lack the caming force of a bolt.
If you cannot find a SB FL sizer die, I would be happy to size some brass for you which you can then reload with a reduced powder charge to perform a ladder test for pressure and function. You could also purchase a box of factory reduced load ammunition if you prefer.
I also suggest you talk to Torfi @ TSE or other gunsmith with a Hawkeye borescope (
http://www.hawkeyeblue.com/page/page/3326819.htm) and ask them to inspect your chamber and locking lugs and to measure your headspace.
If your problem is unsolved after all this then disassembly may be necessary with the previous caution.
Good Luck, YMMV