I don't have any experience with Kimbers, but I own two Rem 700 LVSF's - one in .204 and one in .22-250.
I used the .204 as my #1 calling rifle last year and really liked it. I like the looks, and the gun is nice to carry. I removed the factory pressure point in the stock before did any shooting and mine is a solid 1 MOA shooter with handloads (usually 3/4" - 1"). Trigger was pretty poor, so I replaced it with a Timney.
I liked my .204 so much I bought the same gun in .22-250. I wanted to personalize my .22-250, so I put it in a B&C medalist stock. I had the trigger professionally reworked to about 2.5lbs and it is very satisfactory. I have only shot factory ammo so far, but this gun looks like it should shoot just as well as my .204 once I start loading.
Other than the factory trigger needing work or replacement, I think you would be very satisfied with a 700 LVSF. I did not try much factory ammo with either of mine (only 2 different selections in each), but both shoot about 1 1/2" with factory ammo. If you decide you don't like the factory stock, it is easy to find a wide selection of replacement options.