another one worth taking a look at would be a 7mm-08 . it too is based off the 308 . I now have 3 of these and they work well on whitetails . here is a recoil chart that might help you make your decision . Jim
I would add another + for the 243 over the 260. Not because it's superior, it really isn't but for waht you describe I don't think the 260 is the answer. The 243 with the 80-85gr Barnes loads has WAY less recoil than the 308, I know I own and shoot both.
Before you change your barrel for anything, I would FIRST get a top level recoil pad, like the Limbsaver or Kick Eze. Either one will reduce shoulder pain a LOT. I just added the Kick Eze to my 30-06 and man what a difference. By the way, I go in this Thursday (12/06) for shoulder surgery on both rotator cuff and bicep muscle issue. The recoil of my '06 does not bother either of those, so I know where you are coming from. Mine are not mild loads, I am pushing the Barnes 168gr TTSX over 2900fps.
I also added the Kick Eze cheek rest pad and the combination of the two makes this rifle sweet to shoot. I used to dread range day, but no more.
Try the new pad first, and if that's not enough, you might try loading the 308 with lighter bullets, ie. 125-130gr and matching 260 Rem speeds of around 2900-3000fps. If you reload there are reduced loads published for the 308 by the plenty.
Not talking you out of the swap, just looking at the $$$ aspect of it.
I would also consider the 257 Roberts as well. It will be better that the 260 for lower recoil and can pack heavier bullets than the 243. Many folks consider the 25 cal as the ideal Whitetail caliber.
I own a 260, 7mm08, and a few 308's. I personally can't feel a big difference in felt recoil between a 150 grain 308, and a 140 grain 260 or 7mm08, all other aspects of the rifle being equal. Before buying another rig, and possibly not achieving your goal, you may want to consider recoil reducing devices as others have mentioned. For the ranges you describe, and the size of Carolina deer, you could also consider reduced power loads. For the reasons described, many are down on the use of a good brake, but it is, when combined with a good pad, by far the most effective way to reduce the recoil of a 308 to below 243 levels. During practice, and from prone, ear protection is absolutely required. When hunting, I wear a set of the Silencio, wire connected plugs around my neck. When a shot is anticipated, it takes 3 seconds to stick them in. IMHO, it's not an issue at all.
"Let us speak courteously, deal fairly, and keep ourselves armed and ready"-T. Roosevelt
Since they got you covered on the rifle side, I highly suggest to get that shoulder/rotator cuff problem, it's going to get worst unless you take care of it. Now the .308 is bothering you, next whatever caliber you step down to well also bother you.