Your looking at the right time, the Rainier select 16" barrels came back in stock for the 1st time in months https://www.rainierarms.com/?page=sh...roduct_id=3279 if you don't mind a stainless colored barrel. Surplus Ammo & Arms has the Black Hole Weaponry (BHW) version in a black finish http://www.surplusammo.com/blackhole...artsfinder.com

I have BHW version of this barrel and i highly recommend it. The difference between the BHW barrel and the version made for Rainier by BHW is the Rainier has a little more metal removed and the Rainier has 5 groove rifling opposed to the 3 groove on the BHW barrels. These barrels are pretty beefy and are going to weigh more then the BCM BFH barrels. FYI These barrels do not have true polygonal rifling, the rifling is much more akin to 5-R rifling.
Click image for larger version.  Name: 5rvs6grooverifling.jpg  Views: 28  Size: 90.5 KB  ID: 39213
Rainier uses different company's to make their different grades of barrels (IIRR Shillen makes the Ultramatch, Wilson makes the Match and BHW makes the Select) and i have no clue who makes the mountain series but the select series is supposed to be a step up and in your price range.
Another barrel that would be hard to beat for the money are the White Oak Armament barrels http://www.brownells.com//rifle-part...-_-Custom+Link