After sending Browning multiple letters (via snail mail, cause they were not online) I finally received a voice mail message from a Gentlemen from the company stating, in short.
"Yes, it is physically and mechanically possible to swap barrels with any caliber that uses the same bolt head (243, 7mm-08, 308, 338 Federal) since all of these calibers use the same parent case. Even the Magazine is the same in the BLR.
HOWEVER! He was very specific in stating the the Browning SALES dept. will NOT sell you a caliber different than what the gun left the factory with originally."
To purchase replacement barrels, you must provide Browning with the serial number of the firearm. If the request does not match the serial number of your firearm, the sale is denied.
Now, I received that phone call in 2014. So it MAY be possible that Browning policy has evolved. But current history does not give me hope. You CAN order custom made barrels for the BLR from third parties. 2018 prices for those start around $300 +.
If you read this far, please take the time to write Browning a letter and let them know how you feel about their policy.
One Browning Place
Morgan, UT 84050
customerservice@browning.com