Bubby,
I purposely steered clear of the .270 for my Encores, as I have shoulder problems also. I have a .270 in a Remington 700 ADL, and prior to installing the thumbhole stock and Limbsaver recoil pad, it would tear me up pretty bad in no time. Those two additions toned it down some. They also make reduced recoil loads for the .270, although I haven't tried any yet.
In my experience with prior single shots (mostly H&R's and NEF's), they usually kick fairly well - I would compare them to being the same as a bolt gun of the same weight. The Pro Hunter stocks on the Encore took a bit of this kick away, but I have an affection for laminated wood stocks, so I sold off my Pro Hunter stock and forearm. I've been tempted to reduce my recoil problems by quite a bit by going with a semi-auto, but just can't get myself to do it right now. I like bolts and single shots.
Both of my calibers (.25-06 and 7mm-08) kick considerably less than my .270. I'm really liking both of them, but I'm more enticed by the 7mm-08 right now, mainly because I can shoot a 140 grain bullet from it and it still kicks less than my .270 - that's what I was looking for. The .25-06 kicks less than the 7mm-08, and I think that is because I'm only using 100 grain bullets out of that one (they give me the best accuracy). I like the reduced kick, but really like shooting a heavier bullet. Just personal preference.
On a comparison table (Chuck Hawks recoil tables), this is what is going on with comparable rounds between 120-140 grains out of those rifles:
.25-06 (120 grain bullet at 3000MV) - in a 8 lb rifle, gives 12.5 ft lbs of recoil energy
7mm-08 (140 grain bullet at 2860MV) - in a 8 lb rifle, gives 12.6 ft lbs of recoil energy
.270 (130 grain bullet at 3140MV) - in a 8 lb rifle, gives 16.5 ft lbs of recoil energy
When I first got into Encores, I asked the same question on many sites - What caliber should I get to deer hunt with? I compiled all the answers. It was almost a tie between .25-06 and 7mm-08, with the .25-06 edging it out just by a hair. Next came a fairly close race between .30-06, .270, and .308. There were a few thrown in there that I didn't expect. 6.8SPC is a fairly new round, and available from the custom shop. Too new for me though, and only two people recommended it. 22-250 came up quite a bit, but I wanted something bigger. .243 was a frequent choice, but not as much as some of the aforementioned ones. I've shot .243's before, and wanted something bigger.
Why don't you make a road trip and come shoot one weekend with me?
All the best,
Glenn