Public verbal commitments can dramatically reduce the attention, but only if the student-athlete truly understands what the word "commitment" means. If a kid "commits" to Florida, for example but keeps making official visits to other schools he's likely to get more attention, not less. Now if he had already signed that would be a different story.
Timing is the Key
The biggest reason coaches oppose the notion of an early signing period is that the proposal called for a signing window in December. College football coaches already are saddled with having to scout high school games on Fridays and coach their teams the next day. The last thing they want or need is having to host a dozen or more prospects during each home weekend. A December signing period would also put even more pressure on the high school kids. They don't need that while they are playing their seasons and possibly going after a State Championship.
Instead, I think there should be an early signing period the first week or two of August. You'll have the players' junior year grades and probably the first round of standardized test scores. Summer is an easy time to arrange for a campus visit and you could make a big deal about the first weekend of fall practice to expose the prospects to the program and people involved. An August signing period would give a kid the chance to put recruiting behind him so he could enjoy his senior year in peace.
There would be no requirement for anyone to sign early, that would be absurd. But the same rationale that has student-athletes signing in November in all other sports applies to football players, too. It's time to stop making high school football players second class citizens and give them the same opportunities their prep schoolmates enjoy. August is the best time to do that.