0.2780" is pretty loose for a 270 cal rifle to be honest. Generally with larger diameter bores, a traditional thin jacketed bullet is the most accurate because they will bump up to fill the bore better under pressure then a heavy jacketed bullet or a solid style.
That said, most thin jacketed bullets do not get along well with a fast twist barrel. Bullets such as the Ballistic Tips, Accubonds or something similiar would be my first choice with this fast twist barrel to see if you get any accuracy results at all.
You will not be in the velocity relm to really tear apart most conventional bullets so it may just be a trial and error type deal.
In all honesty, you need some heavy bullets. The problem is that the 270 Win is not really large enough for some of the real heavy pills.
I would recommend dropping Richard Graves an e-mail at email@example.com
He makes a 169.5 gr ULD RBBT that would be perfect for this rifle, that is if the large bore diameter will shoot these bullets accurately. THis is about as heavy of a bullet as I would recommend with the 270 Win but they should work very well and with a BC in the .7 range developed from actual bullet drop, they will offer ballistic potential far higher then anything else out there in the 270 cal family of bullets.
This twist is designed for heavy, long bullets, not sure why it was selected for a 270 Win but this is what I would recommend to try to get it to work.
Drop Richard an e-mail and see what he has to say.