The specs on McMillan's site leave much to be desired. The light varmint will absolutely work in the classic. (unless the Criterion version is a really a huge departure from a 700 LV)
Give them a call.
The REMAGE Criterion light varmint contour runs basically 1.057 from the front of the threads to .803 @ muzzle @ 20"
I was also interested in the Remington "Compact" stock but info on website says will only With barrels up to #3 contour.............then again the REM Classic says only #5 contour but apparently that is inaccurate if a light varmint will work in it.
Would really rather use the compact stock if it will work but would be content with the classic.