Re: BAT or STILLER VIPER FOR F-CLASS?
Have you considered a Barnard, Stolle, or for that matter, Savage, action? I couldn't tell you the numbers for the F-Open team, but at the recent FCWC, the USA F/TR team fielded five Savage target actions, four Barnards, and one Stolle Panda. No Remchester clones - although I've seen enough of those shoot as well to not discount them either.
I have a Stiller TAC30. Lots of drama around actually getting the dang thing in my hands. Shoots great, but I don't think I'd buy one of their products again, unfortunately.
One guy I know, very serious shooter (Felix 'Bud' Solis, you might have seen him in a recent Berger bullets ad ;) ) has something like six or seven BAT actions last time I asked - obviously he loves 'em. Chambered in everything from .223 to some moderate thumpers (Bud shoots from a sling, so no muzzle breaks), very smooth, exceptionally accurate.
Barnards are a little less pretty to look at (kind of like Savage ;) ), but with the deviation between the euro and USD, the RPA Quadlocks have been priced out of competition, and the Barnard comes with a very nice functional trigger installed - or you can hang any 700-compatible trigger you want on there. Right bolt, left bolt, left port, right port, dual port, mag fed, etc. They make 'em all. They seem to be one of the current darlings for the long-range prone (Palma/F-TR) community.
I'm pretty partial to the Savage target action - order one, get in line for a true-n-time job @ SSS + one of their 2oz triggers, order a barrel, stock, etc. wrench it all together, start shooting. When your turn comes up @ SSS, send off the action and when it comes back it'll be all slicked up and shooting even better. Maybe not as slick as a BAT, but there's a price differential of 3-4x there...