The 600/660 did not use the same action as the 700, it used the same action as the Model 7.
Slight mixup there. The model 7 is a much later design than the 600/660 rifles. The model 600/660 used the same action as the XP-100 pistol (or vice versa, not sure which one actually came out first). The model 7 uses an action the same length as the 600, but I don't know if it is the same action. Will take me a couple days to check with friend who has model 7s.
The 600s use what looks like a short 700 action, but there are some differences in the action itself. The bolt is the same design as the 700, other than the bolt handle. Early 600s use a cocking piece shroud similar to the model 721/722 in appearance. Later ones use a shround that looks just like the model 700.
Model 600 series rifles are somewhat collectible, I have 5 currently, .222, .243, 6mm, .308, & .350, and am looking for a 6.5mm.
For a project gun, if you can find a 600 or a Mohawk at a decent price, fine. But the odds are against it. Get a new model 7 in .243 or .308 and you might just find its all you want in one package.
OR, look for a used 700 short action. Lots of them on the used racks around the country, often for fairly cheap, considering.