You should straight up go to Princeton and give some lectures about this before they call the police.
Finding more than 1 (a prefix of length 3) in 4096 is rare, and omitting the target is even rarer. The length of the prefix doesn't matter as long as the block matches what's expected.
Nor do you try as much as you try, the probability will remain ≈ the same.
If finding more identical prefixes within 4096 were no longer so rare, the hashes would be broken.
I will again state that you don't really understand how an uniform distribution works. You're simplifying to a yes/no gambling, forgetting completely about the basics of it.
If finding more prefixes in some portion means the hash's broken, man, please don't make me provide actual examples about how wrong you are.
When you skip some rest of "block" as you call it, you simply move off the chances of finding (or not finding) another prefix, into the next block. Basically, a futile operation to perform, because it goes the other way around too: when you fail to find some prefix in the next "block" or whatever, it might simply mean (at an average level) that it was found in the skipped portion. Or any other portion, anywhere, to be honest. Because, for the 9000th time (for you): it's an uniform distribution, all keys are as likely as others, and all ranges are as likely as any other ranges.
So you're simply selling some illusion of some sort of benefit, but it does not exist, neither in theory, nor in practice. It would be great if it would, though.