No need to move the location of the kick. Just limit the kicker to 2-3 steps before kicking like in a EP or FG. He will not kick it as far. Also limit the kicking team to a 5 yard run up to the ball. Maybe it will slow them down a little and there will be less injuries.

The second of your suggestions was already added as an NFL rule this year (6-1-3a)
As for the KCI or the ball touching the ground and going 10 yards, neither are NFL rules.
In the NFL, the only requirement is that the ball be past the plane of R's restraining line. If it is, it is a free ball, equally available to either team. It need not have hit the ground.
As for TxMike's original comment of not seeing the advatage, the issue lies in the NFL rule that says no tee may be used on safety kicks. Your options are a punt, a drop kick, or set the ball on the ground. Given that they wanted an onside kick, the drop kick was probably the best option.
I understand this is an NCAA board, but the discussion is around an NFL kick, and too many NCAA rules are being applied. This is an area where the NFL differs greatly.