Like several posters before me, I'm going to try to change your view via an alternate proposal.

I agree with you that the barrage of fouls that tends to come toward the end of many games can get extremely tedious. However, I agree with others that a reasonable amount of strategic fouling can enhance the excitement of the game, while running off time strikes me as having too much potential for anticlimactic endings. I'm also not comfortable with your applying penalties differently depending on which team is in the lead.

So here's the idea I'd like to float…

Apply the following penalties during the last two minutes only to all defensive fouls on players not in the act of shooting:

1st such foul committed by a team: opposing team retains possession and inbounds the ball (as is currently the case)

2nd such foul: two foul shots (no change there, either)

3rd such foul: two foul shots plus one point awarded to the fouled team

4th such foul and beyond: two foul shots plus two points

I feel that, after a reasonable point, this approach quickly sweeps away the incentive to intentionally foul, but still makes it worthwhile for a trailing team to play hard defense and go for steals — the game won't just end if they get too aggressive.

(Incidentally, I also like this "awarding of points" approach for individual fouls — maybe instead of hampering players with the prospect of fouling out, you start awarding points to the opposing team after a player's fourth foul and gradually increase the penalty. In an important game, I'd like teams to have to decide whether keeping a star player in is worth giving up a few extra points per foul rather than having him just sit on the bench in foul trouble.)