One more adjustment!!
Plank Road Farm--According to the Lyman's 49th ed. Reloading Handbook, the 6.5x55 Swede has a case rim diameter that is 0.007" larger than the case rim diameter if the .270 Win.
Soooo, depending on how tight are the bolt face rim, and the extractor, of your Savage M-110, you may have to open either or both of those up just a tad to accomodate the Swede cartridge.
Neither adjustment is impossible, just be aware that they may be necessary.
While I'm at it, I agree with the above posters who state that there isn't much difference between the 2 rounds in terms of ballistic performance. Frankly if it were me, I would NOT do the switch, just because there is so little--if anything--to be gained.
Unless of course, the .270 bbl is shot out or otherwise ruined, or if you want to just for the experience, regardless of the expense, hassle, and lack of benefit.
Another thought: You could rebarrel to something else with the same size case base as the .270, and then it becomes a simple bbl swap, nothing more. If you want a 6.5, the 6.5 Creedmoor comes to mind; it is based on the .308 Win case, which has the same base as the .270.
However, I still wouldn't do it, unless you want to "just because." If I had a good, accurate shooting .270 with irons that I wanted to modify, I'd put a 'scope on it but that's all. Use removable rings, leave the irons in place, have the best of both worlds. (Please, no tip-off or "see-through" 'scope mounts!) The .270 is a useful short to midrange to what many people would call long-range cartridge, and will put down deer, antelope, and the like, as well as 10-rings, with regularity--always given that the shooter is capable!
Anyhow, good luck with the .270, whatever you decide, and PLEASE keep us posted, preferably with pictures!