There are some really good bullets of the <121gr variety that you can use for the 1:11 bbl that you have. The 85gr would be too light for your application. Barnes does make some TSX and TTSX in .277". Remember that the "no lead" style of bullets will be somewhat longer than the copper jacketed lead variety.
I killed several hogs with the 120gr Hornady SST but I wern't pleased with them because every one of them shed its jacket.
If you give the Barnes a try,remember NOT to seat the bullet so that is tight to the lands. Barnes reccomends a slight jump into the lands for their solid copper bullets. --- SAWMAN