Global changes I'd like to see for football (all levels here) --
KICKOFF ELIMINATION AND REPLACEMENT
Kickoffs are eliminated. They're very disproportionately dangerous plays because players run into each other at a full sprint. Onside kicks are also stupid/random and never seem to work out.
Instead, the team that would have had to kick off under the old rules (the scoring team for TDs and FGs and the scored upon team for safeties) is given the ball on their own 35 under a 4th and 10.
They can either punt (and a longer punt like that has some chance of being returned, which preserves the return game, certainly more than almost-automatic kickoffs into touchbacks does) or go for it. The punt is safer for special teams players because they're lined up right in front of each other at the snap and the returner can fair catch/is protected. Going for it on "4th and 10" is an interesting comeback mechanic --
-- while they would be rare, ten yards is not too far for the occasional fake punt gadget
-- plays from scrimmage are less random than an onside kick
-- offensive and defense stars are on the field, not no-name special teamers
-- ten yards leaves room for some diversity in the playbook (e.g., the screen game)
-- ten yards is difficult but not impossible to convert in one play, which means the attempt is going to be worth it for teams in desperation mode needing the ball back
-- at the same time, the chance of not converting is high and the field position penalty of giving the opponent the ball amid your 35 and 45 is not going to allow this to be a standard
ONE AFTER TOUCHDOWN FOR FREE
This is to speed the game up. When a team scores a touchdown, they can elect to receive one point for "free" (no need to kick the PAT) or they can line up from scrimmage and go for two. This deemphasizes the role of kickers, sure, but only in the boring ways that waste time they are being deployed under the current rules. They would still be necessary for field goals, though, and all the exciting drama that brings.
OVERTIME SHOOTOUT
I'm stealing this from association football and penalty kick shootouts.
In the event of a tie, the two teams each have five attempts at a two-point conversion. The game ends when one side is mathematically eliminated from at least tying the number of successful conversions made by their opponent. If tied after five, then do rounds until the tie is broken -- sudden death.
Exciting and quick, right?
I have heard soccer and hockey fans bemoan penalty shootouts because it is a "warped" version of the game. PKs do not resemble the real "heart" of the game of either live-ball action on the field or the set pieces involving the whole of both teams. I can see their argument there about it being "artificial."
This is not an issue with American football. Running plays from scrimmage, and either moving the ball or stopping its progress, is the core of the sport. Testing the two team's relative abilities to either score touchdowns or stop a score in short-yardage goal-line situations is a worthy test of that. This is not artificial.
So yes, build overtime around that pitched battle.