If recoil is such a big deal then just use a recoil pad. If you were thinking of getting the .270 win then consider that cartridge has about the same recoil of a 308 and 30-06. It usually depends on what kind of rifle you have that determines the recoil. If the rifle is light and has a short barrel it is going to kick more. But those three rounds are very similar in that aspect.
Well, yeah, but then recoil tolerance is subjective. I've been pelted my whole life with goose loads in 12 gauge and recoil is just one of them things you put up with for me. I don't happen to think my 7 mag is all that bad. I've fired up to 375 H and H and not seen a problem with it. Yeah, it pushes ya back, but just roll with it. My little M7 is light and short in .308, but I can sit down at the bench and shoot it all day long. It don't feel that bad to me, lighter than the big 7 anyway, LOL. When I'm bench shooting magnums, I wear a Past recoil shield, but I don't need it in the field, don't even notice the recoil when I'm shootin' at game.
But, you're certainly right, if a person doesn't like a lot of recoil, you can make the gun heavier. There are ways of doing that to an otherwise light gun, like adding lead to the stock. But, a heavy barrel gun will run the weight up there and a big, heavy scope. There are lots of "sniper" or varmint/target heavy barreled rifles to choose from. Of course, if you have to tote that thing over mountain passes, it can be a pain. It's a trade off, I guess. I accept the recoil of the .308 in the M7 (not that bad) for the light weight and handiness of the rifle. It's a sweet shootin' little rig. In .260, it'd recoil less and probably shoot further considering the BCs of .264" bullets. I think a .260 is all you need in Texas, too. I got the .308 before the .260 came along, but I sorta wanted .308 anyway. It does everything I need it to do.
One thing about .308, if you don't handload, you have a heckuva selection in loads to choose from, probably more than any other caliber outside of .30-06. That might be handy just to find a load that will shoot under 1 moa (what you need for long shots you're talkin' about). With a limited selection of loads, might be hard to find a good, accurate load. I handload so that's not really a consideration. I have very accurate pet loads for my rifles and they cost a lot less per round than Federal Premium.