You have this selection of .243, 260 (which is a 6.5/08?) and a 308 barrels, and none of them do what you want!?, man are you picky.
I suspect that since a 6.5/08 will feed through a FAL that you won't have problems with 7mm/08, but nothing in gunsmithing is assured. I also suspect that the adjustable gas port may be really helpful.
I have never rebarreled any of my FAL's and don't want to. I am happy with the 308 caliber. However I have rebarreled M1a's and Garands.
Let me tell you, gas gun barrels have to be made by someone who knows what he is doing. It is not like a bolt gun where you take a tube, turn it to shape, thread the ends, crown the muzzle, stick a reamer up the back, and you are very close to a useable barrel.
Military gas gun barrels have all sorts of threads, attachment points, cuts and slots, gas ports, etc. All have to be correctly cut and lined up or the barrel is no darn good.
There are very few people who make M1 and M1a barrels, I suspect the list of people who make FAL barrels is even shorter, and it is because it is not a simple task.
Why don't you just screw on a nice 308 barrel and be happy?