The action is the same. The only parts that change are the barrel, the magazine well spacer, and the magazine. As long as you get a barrel with the same contour as your initial model, everything will be fine. I agree with DPris that a bedding job that extended under the barrel might not interchange well.
In terms of stabilizing the stock, my experience is that two things were worthwhile:
1) replace the bottom metal with new bottom metal from DIP. This is admittedly maybe partially cosmetic, but I didn't trust the old part.
2) add a 3" inner-tube rubber shim between the barrel and stock on the first 3" of the barrel.
I would then set the action screw torque to only about 15-20in-lbs. The 25in-lbs CZ recommends is WAY too much.
I've done a lot of experiments with mine and determined that that gave me the best combination of bench accuracy and accuracy from slung field positions, which is my objective. Some people recommend shimming or bedding the whole length of the stock, but I found that gave me about an 6MOA POI shift between slung and bench, which was obviously not acceptable. With the 3" shim I get no visible shift, and comfortably sub-MOA groups.
Given my current results, I don't intend to pillar or skim bed the rifle.