Buyers:

http://www.tf2outpost.com/trade/24575670 2 ref

http://www.tf2outpost.com/trade/24624909 2 ref

http://www.tf2outpost.com/trade/24702951 2 ref

http://www.tf2outpost.com/trade/24704793 2 ref

http://www.tf2outpost.com/trade/24700480 2 ref

http://www.tf2outpost.com/trade/24601713 2 ref

http://www.tf2outpost.com/trade/24582047 2 ref

http://www.tf2outpost.com/trade/24680325 2 ref

http://www.tf2outpost.com/trade/24565630 2 ref

http://www.tf2outpost.com/trade/24624783 2 ref

http://www.tf2outpost.com/trade/24696883 Trade offer sent at 2 ref after first bump

http://www.tf2outpost.com/trade/24699281 Sold at 2 ref after second bump

http://www.tf2outpost.com/trade/24665220 2.11 ref

http://www.tf2outpost.com/trade/24652969 2.66 ref

Sales/offers above 2 ref:

http://www.tf2outpost.com/trade/24221657 3 ref

http://www.tf2outpost.com/trade/24667603 4 ref? (has another in bp and the one in trade wasn't whited out so not sure if there actually was a sale)

http://www.tf2outpost.com/trade/24659307 5 ref?

Trades to watch:

http://www.tf2outpost.com/trade/24704252 Seller at 3 ref

Conclusion:

Vast majority of Blighted Beaks on Outposts are painted, and some are looking only for CS:GO offers or some kind of offers/item overpay, so I gathered practically every valid trade that wasn't highballing or asking for something besides metal. Currently none on Outpost are available for 2 ref, and the large amount of buyers at 2 ref indicates that the current price is a quicksell. The 4 and 5 ref possible sales are vague so I did not include them in the range. Though proof is limited due to majority of the sellers having painted Blighted Beaks or asking for other items, the 2.66 ref offer and 3 ref sale seem to make 2.66-3 ref an accurate price range.