To move up, the C's have a lot of assets at their disposal:
1) Their 4 picks this year.
2) One of the 2016 firsts (Brooklyn, Dallas, or our own).
3) One of Sullinger, Olynyk, and Zeller
4) James Young
5) The Minny 1st/2 2nds
6) Our myriad of 2016 2nds
7) Our more distant 1sts
Our trade exceptions to absorb salary
For example, in 2013 we held pick #16, and it cost us two 2014 2nd rounders to move to #13. That is a very easy price to match again if there's someone who slides into the late lottery that piques Danny's interest, as we have four 2016 2nd-rounders, not including the Minny pick. In 2011, we dropped from 25 to 27 for a 2014 2nd rounder. Moving up a couple spots from the Clippers pick is also easily affordable. In other words, I think it's pretty easy to move up 3-5 spots from both of our current selections without sacrificing anything more than 2nd round picks, or at most the Minny pick. And depending how the draft falls, that may be enough to get a very good player.
To move into the 8-10 range, I think it would cost us #16, the more favorable of our 2016 pick or the Dallas 2016, both Top 7 protected, and one of our 2nd rounders from Philly. To move to the 6-7 range, I think it's the above, plus a player on a rookie contract (Young, Olynyk, Zeller, or Sullinger). Possibly the Philly 2nd wouldn't be needed in this case. To move into the 3-5 range, I think it's #16, the best of our 2016 1sts (Brooklyn, Dallas, our own) with no protection, a rookie deal player that isn't Smart, the Minny pick, and probably a more distant first like the Memphis pick. I don't see any team with the top 2 picks trading it for a smorgasbord of lesser picks and young players. #3 admittedly might be a stretch as well, but I think it depends how the lottery shakes out. For instance, if Sacramento slides up to #3, do they really need to pick their 3rd SG in a row with a top 10 pick (choosing Russell), or might they be willing to slide back this year and acquire a bunch of other pieces, considering they owe multiple future picks?
Anyway, while it's certainly no guarantee the C's trade up (it does take two to tango, after all), I think they can easily move up a few spaces on both of their picks, and get into the top 10 without paying a price that isn't affordable. And if Ainge identifies a player he thinks is truly special and one he can build a franchise around, he can get that player too, as long as that player isn't Karl-Anthony Towns.