I still think the biggest move to help the defense is improve the defensive rebounding. Two many 2nd, 3rd.... shots after playing good defense on the first shot.
I think that's the big issue.
Here is Basketball Reference's Four Factors for the Celtics' defense:
eFG% 0.503 (5th of 30)
TOV% 0.127 (16th of 30)
DRB% 0.753 (27th of 30)
FT/FGA 0.223 (23rd of 30)
I'm sure that some people will have quibbles with BR's math, but I think that we can agree that other methods will at least give the same general result.
What this tells you is that field goal defense is top 5. That is the most important of the Four Factors, so any personnel changes should not be to the detriment of that, which is already working.
Weakest is, as you point out, defensive rebounding. I think that we can assume that improving that would also affect FT rates - offensive rebounds result in a disproportionate number of foul calls.
Looking at these data, you would not conclude that Rim Protection is the big priority going forward. But you would also clearly not want to give a guy a lot of minutes simply because he improves your defensive rebounding (a caveat about Zizic, for one).
Boston was middle of the pack in forcing turnovers. I would suggest that this is not an area that needs special attention. Of course it's better to cause more, and given Ainge's emphasis on team speed and the youth of the roster, it might be a little surprising that the number isn't any better than it is. But nothing trumps good position defense, rotating, and closing out, and you trade middling turnovers for good field goal defense anyday.
It also should be mentioned that these numbers are for the whole season, and one thing about the Celtics this past season is that they were disastrously bad before New Year's.
As for personnel, does Blake hurt your field goal defense? I think that it would work, while he would improve the defensive rebounding.
Millsap definitely improves your field goal defense, though by himself he doesn't move the needle on defensive rebounding. These things interact, so perhaps his defensive contribution would help the team's defensive rebounding.