Kimber barrels on their hunting rifles tend to be on the light side, as far as profile goes.
They do this to keep them light.
I have an 84L chambered for the 270Win, lazer accurate for the first 3 rounds then it tends to get hot quickly and the fourth shot moves out of the group about a half inch. Fifth shot way out.
I was thinking of having that barrel sent for re heat treating to normalize the steel, but with all of the hassle with sending across the border I'm just going to stick with it as is. It's a hunting rifle and not intended for shooting extensive strings.
The #2 profile would be the lightest I would consider. The extra couple of ounces isn't going to have much, if any affect on carry and will help a bit with stabilizing harmonics as well as aiming. As far as your barrel channel goes, it would be a very quick and easy job for any smith with a barrel channel tool to clear away enough wood for your new barrel profile.
If you're handy at all, a barrel channeling tool's cost is under $40 delivered and it will leave a lovely smooth surface in the channel. Job takes approximately an hour, including set up in the vice and sealing the surface.
If I may suggest, finish off that barrel at 24 inches rather than 22 inches.
The 6.5x55 has enough case capacity for relatively slow powders, such as IMR7828ssc and will give you ''safe'' velocities around 2800fps from a 22 in bbl with 140 grain bullets. This load wouldn't be safe in the older M38/96 Swede Mausers but in strong actions such as the 98 Mauser, Rem 700, Win Mod 70, Zastava M70 and the Kimber M84L it's well within their pressure limits.
Because of this handy case capacity, the extra two inches of barrel length gives a very good velocity increase.
I have an acquaintance with a rebarreled Tikka T3 which has a 1-8 twist, Lothar Walther 24 inch barrel. He dropped the rifle off his tractor and bent the original barrel.
His rifle, with my handloads, built for my rifle, will give him 2950+ fps in the spring with temps around 17C. My rifle, which has the same twist rate but is only 22in long will give me just slightly over 2800fps.
No, I'm not going to rebarrel my rifle. It shoots better than I can hold, under an moa out past 300m.