If the customer pays the account in full, can we wait for the check to clear before we file the release, or does this have to be done right away?
The state of Florida has no specific provisions regarding the timing of a lien release. As the article linked above explains in more detail, sometimes the battle of "who goes first?" can get tricky.
However, if you've already received a check, then the leverage is all on your side. Best practice would be to wait until the check clears. I've heard too many horror stories of contractors releasing their lien claim, and the check subsequently bounces; leaving them with little recourse besides more costly litigation.