I do not have extensive experience with the CZ's but some rifles / barrels, for sure - want some "up" pressure at the forearm tip - I had a 7x57 Ruger #1 that was like that - I noticed much better groups with a bedding pad at front forearm tip than when that barrel was "free floated". It was maybe all in my head, but typically holes in targets do not lie. I am not sure that contact on one side and not the other is a very good thing - but, my own experience is that "up" pressure - "bedding" pressure - on a barrel can be really good. I have very old - circa 1900 - rifles that are in full length contact between barrel and entire stock - must have been a touchy and skilled labour intensive thing to do to get "even" all the way - and then very much subject to bedding going "sour" with any distortion from moisture gain or loss within that wood stock, or whatever. I suspect that "free floating" is cheaper to do and takes less skill - and results about the same. But is not "slam dunk certain" that free floating gives best groups - you have to fire it to see what your's wants.
Thinking - might be also about your need - my concern was mostly about hunting - so my concern usually where would first, maybe second or third shot go - was not a concern for me about first 5 shot group versus 4th 5 shot group - and that may alter what works well.
It may or may not be relevant - the British Army standard called out .030" free float for the barrel within the hand guard and fore arm for the No. 4 Lee Enfield - but solid bedding at the knox form and "up" pressure near the front sight. But those rifles were made to be capable of sort of 3 MOA or so, so maybe not a thing today - but, to be fair - also had to serve as a bayonet handle, so maybe is more involved than simply "best design" to fire rounds. I believe 1950's and 60's target shooters improved that with "mid-bedding" and sometimes a "packing" within the hand guards - so is "sort of" an example where a more or less "free floated" barrel was made to shoot better, by adding more bedding, at more or less precise points along the barrel length.
Is also the "silk purse" versus "sow's ear" thing - from target shooters, I understand that despite best efforts - some barrels do not shoot well - can be made to shoot better, but not "best" - why barrels are often changed out - another barrel often resolves their issues. Is way beyond anything that I have tried, but I read that some buy three barrels at a time - try each one - select the "best" of them as their target barrel - even when barrels made sequentially in same plant, are apparently different, one to the other.