This has obviously been covered in other threads, but I don't feel like I've been watching the same games that you have. Against Notre Dame, Vermont, and Kansas (and perhaps a couple other games), our perimeter defense was awful. As far as opponents dumping it down to the low post, there's a whole thread on this, which play-by-play stats, that seems to show we're not getting hurt that badly in this area.
We've covered the three-point shot fairly well all season, and we had a great deal of defensive improvement from Alabama through Elon, but in the other games we've done a poor job staying in front of our man on the perimeter, a poor job staying with our man off the ball, and a poor job communicating and rotating. It's certainly not all about "interior defense and rebounding."
Except this really isn't true, either. We may not be a great defensive rebounding team, but Duke ranks 74th in the country in defensive rebounding percentage, which is pretty good, especially for a Duke team. In fact, so far this season we've rebounded on the defensive end better than any Duke team in at least the last 17 years and maybe in all Coach K's time.
Again, this has been gone over ad nauseam in other threads, and again I feel I must have been watching different games than you have. I know you can't teach height, and he may get there eventually, but right now Marshall Plumlee does not appear to be a very good defensive player. There's no evidence that playing him 15 to 20 minutes would improve our defense, and it's at least equally possible that it would actually make things worse defensively. Plus, there's almost no chance of it happening.
You say we have only two choices, but you've left out what Coach K has been doing all season, namely playing/starting Tyler and Josh to shore up the defense and using Rasheed and Andre to bolster the offense off the bench. You may not like it, but not only is it an available option, at this point it seems like the most likely option. Certainly about a zillion times more likely than Marshall playing half the game.
Sure, Amile might at some point replace Josh in the starting lineup -- Amile has been rebounding ferociously since the third game of the season. And, yeah, it's possible Rasheed replaces Tyler in the starting lineup down the road. But if those things happen, Tyler is still going to get 15 to 25 minutes, and Josh will probably see 8 to 15. No analysis that completely ignores our seniors is going to come true.
Also, as opposed to "simply attempt[ing] to out-score teams," I assume Coach K's strategy will be to continue to try and mold this group of players into a team that can defend. Our players should be able to succeed in this area, they just haven't gotten there yet. That's what I see, anyway.