superlooper,
Welcome to LRH. That's a nice rifle you have there. That was my Dad's pick also. He liked anything John Browning made but picked the BLR because he was a lefty.
For breaking in a barrel I usually clean after every shot for the first 15-20 shots, then after every 3-shot group for 15-21 rds. After that it really depends on the rifle and how quickly it fouls up and the accuracy goes south. There are probably tons of info on there about breaking in a barrel. Some of the barrel makers (Lilja, Kreiger, etc.) put recommendations on their websites for their barrels but it can be modified and applied to any barrel.
I shoot the .243 alot and with the 85gn bullet you should easily be able to achieve 3200fps with good accuracy. I am currently shooting the 95gn pills at 3100fps but as soon as I get my back stops/ranges set up here in Ga, I'll be working up loads with the 85gn BT HP GameKing's.
I have heard the .243 is a barrel burner but I haven't had that to be the case as I have never shot one enough to toast it. My current .243 I bought used but not hurt and I have run about 750rds through it. It prints 1/4" groups consistently.
My Dad burnt out the barrel on his BLR in .243. I really think he just wanted a longer, custom barrel. He sent his to McGowan Barrels and they screwed on a Douglas (I think), 26" light varmint. It was remarkably accurate when he first got it back but I haven't seen that accuracy since he left it to me, but I really haven't tried or shot it very much. I'm not sure how many rounds he has down this tube.
I don't know that there is a specific velocity that burns a barrel out. There's gonna be alot of heat when the cartridge goes off no matter what. With that said, if you start approaching 4000fps, as you will with 55gn bullets, barrels don't seem to last long. Not sure if your rifle will be able to approach that velocity as it's 22", isn't it? Anyway, give them a try, keep your barrel clean and cool and you should be OK. JohnnyK.