Yes, you should rewrite the beatsheet.
It is a way of planning the story, but for reference you should keep it current with the story. The beats do matter, and your 12 beats or 40 beats or whatever you use should reflect that.
Readers expect certain beats at certain points in the screenplay. They don't have to be absolute pinpoint to the page, but they should be in order.
If you are moving scenes around offbeat for logical justification, I'd worry you are weakening your story, skipping beats and jumping the gun. You might need to rethink that.
Sometimes a beat can be skipped, or implied. Sometimes a beat can be accomplished with a single line of dialogue. There are no ironclad rules. But professional readers know "good" stories so well they have internalized the way good stories are told; and that is why pros have distilled that knowledge into beat sheets.
In other words, they aren't arbitrary rules that were handed down from on high, they are the scientifically distilled experience of professionals on how, on average, commercially successful stories are constructed.
Following them gives you a better chance of writing a commercially successful story.