Of course, the primary motivation for any change must be to increase scoring. It is my view, as an American, that increasing the probability of scoring decreases the probability that a bad call or a lucky break will ruin a game. Basketball, (real) football and hockey get it right.
I think there should be two simple rules changes. Both of these changes center around a new line "near" the goal. This could be the inner box, extended, or it could be the outer box, extended, or it could be a new line somewhere in between. I will call this the Near Line.
Elliott's First Rules Change: More Corner Kicks
A ball that is kicked out of bounds by the defense beyond the Near Line (that is, closer to the goal) results in a corner kick by the offense.
Elliott's Second Rules Change: Screw Offsides (sometimes)
Offsides is not called if the ball is kicked from inside the Near Line.
Impact of These Rules Changes
One of the best opportunities for the offense to score is the corner kick. Increasing the number of corner kicks will increase scoring. This rule change will likely lead to an adaptation by the defense to kick the ball well past the Near Line, so it may not have much impact.
Offsides is one of the strangest rules in any sport (aside from some of the rules of baseball, of course). Although the actual intent of the offsides rule is not clearly stated anywhere, it seems to be there to avoid creating a situation where an offensive player stations him/her self near the goal, waiting for the easy tap-in. (This does not seem to be a big problem in, say, basketball--whatever!) But once everybody else is already near the goal, calling offsides is a pretty crazy (and error-prone) bastardization of the (probable) intent of the rule.
If the ball is close to the goal, the defense should be punished! Get rid of offsides near the goal.
As for the position of the Near Line, I think that the small-box-extended is probably too close, and the big-box-extended is definitely too big. Drawing a new line on the field is just (uh) too American. So I think I'd favor that the Near Line be the small-box-extended.
With these simple rules changes, the 0-0 tie, settled by penalty kicks, would become a thing of the past. There would never again be a botched call in a World Cup game, and peace would come to the Middle East. Cats and dogs would sleep together and road construction would be completed in Chicagoland!
Well, maybe not that last one.