If you rebarrel it would make building a 25-06 modernized easy. Go 7 or 7.5 twist and throat it for the new 25 cal "heavies".
Odonata, this statement is personally significant. Back in a former life I was a huge (YUGE) 25-06 fan. I did most of my killing with 100grain pills from prairie dogs to big deer, even an elk. Light/Fast/Flat .25 cal can be pretty damn impressive for what it is. But after committing to that caliber and wearing out several 25-06 barrels over 25 years these are my conclusions:
1. If I'm going to shoot p-dogs/coyotes, my 22-250 is just as flat, just as devastating, and I get to watch more rather than losing the image in recoil.
2. Neither cartridge recoils all that much, but any volume of shooting and the 22-250 is less tiring by a lot.
3. 25-06 is better on paper than the 22-250 especially in the wind, but I can't say it practically ever mattered on big or small game.
4. Antelope and Deer were nearly always very satisfying results with the 25-06. Big bodied deer, elk, longer ranges, tough shot angles is where it quickly ran out of oomph. At least with 100gr bullets. A modern bullet mighta helped a bit more, but that's all in the past so I'll never know.
4.5: I've only ever shot two medium deer with 22-250. 55gr soft points worked fine, but I'm confident it woulda worked more-finer with a fast twist and a heavier bullet. But no complaints but also no urge to do so on my part.
5. Large charges and slow powders in my 25-06 pushing max velocity also pushed recoil and muzzle blast to be nearly indistinguishable from a 270. A heavier .270 bullet probably woulda been the more capable projectile for every hunt memory linked to item #4.
6. 120 grain bullets were the only ones available back then. But the performance of them was so lack luster on targets and on game that I dropped to 100gr and RL 22 and never looked back. My barrels twist was 1:10 iirc.
Conclusions: Here's the thing, if you go to all the trouble to get a 25-06, load up a heavy 130 "heavy" you'll have a rifle that's ballistically indistinguishable afield from a .270 or your beloved 6.5x55. That's just reality. And in a comparison of those three, the reduced muzzle blast, control/follow-up ease should favor you 6.5 Swede.
Now, rewind 300 posts back to your original quandary... you really need to pause and ask what a 25-06 will do better than your 22-250 and 6.5x55? Probably not a thing... BUT it likely could replace both those guns if you wanted it to! And that fact I think that might-could the real magic of the .25-06 loaded light/fast/flat. It fills a really wide niche extremely well in capable hands.
Get what suits your fancy!