I started out years ago towing our 7,000 lb trailer with my old chevy 2500 with the 350. I tow mostly in the Sierra and Rocky Mts. I hated the way I had to slow down to 45 mph going up the grades. So ...
If you are towing at elevation, I think you are expecting too much from the engine.
As far as it being bad to let a diesel sit, that has not been my experience. My truck sits pretty much all winter. So did the one before it. No issues here.