They ought to do like Rugby. In a rugby conversion, the player can convert the extra point with a kick from any distance on a line perpendicular to the goal line from the spot where the ball was touched down. So if in the NFL, the ball broke the plane for a TD on the sideline, the ball could be placed at the sideline on the 1 and kicked between the uprights (you'd need a wicked curve), or the kicker could place the ball anywhere down the sideline in order to get a better angle.
Now, here's the thing: you have to make room for the both kicking units. SO, LET'S USE MATH. Make the goalpost rotatable on its vertical axis! This way, the kicker and the kicking unit can try the PAT from the hash marks or the center of the field like they normally do. The goalposts will rotate to simulate the angle of the kick, and the more squared-up you request the goalposts, the further away you must kick.
Gather all the data from the last 25 years to see the distribution of successfully kicked FG distances. Find the median distance; make that the center point. Maximum kicking distance can be 2 standard deviations from the mean, and the minimum where the ball is currently spotted.
This would be a neat, if complicated system. It would discourage players from running out of bounds and would probably keep the clock running and the games a bit faster.
Or, you know, they could just not **** with it in the first place.
