Whatever yu get, get something that doesn't need after market product's of reduced reciol loads. If Elk is on your adgenda, I'd first look at a 6.5CM or even 260 Rem. If you reload I'd start with the 260 Rem. A 130gr bullet will work very well on even an elk and there's also 140+ gr bullet's.I have shot two elk with my 6.5x06 and 140 gr bullet, ripped the earth right out from under them. If elk is on the list, I wouldn't drop down so far as the 25-06. Problem for me is the bullet weight's. While killing elk isn't all that hard with a 25-06, it simply run's out of steam for me. Same with the 243 even to a greater extent, 243 is legal for elk hunting in Oregon. No doubt in my mind it would work but I have better.
If from the 26 cal you go up, the 270 can be problem for people with physical problems. Same with the 28's but the 7mm08 sounds t be very easy on recoil. Have head very few complaint's about it's recoil. Case size, think case size. 243, 260 and 7mm08 are all on the 308 case. I have read where the 6.5CM is on a 30 cal wildcat case but people say you can reload them with the 308 case also, I would not try it! Couple other's you might consider are the 6.5x55 and the 7x57. But for recoil I'd still go with a 250 cal.
I have the 6.5x55 right now and it is very comfortable to shoot. I've also had several 7x57 and they also are comfortable, for me that is, I don't have your problem. Strongly suggest you don't get some thing that may need after market items to control recoil and on't get something you need reduced recoil loads for. I don't know a lot about reduced recoil ammo but strike's me that if you have 270 using 130gr reduced recoil loads, if they make them, your way ahead of the game to simply get a smaller cartridge that use's regular factory. If you want a 30-06 but can't take the recoil, don't get reduced recoil loads, get a 308!