If Perk, KG, and Sheed all play 30 minutes per game which is about where each of them will be likely, when all are healthy that leaves a whopping 6 minutes for that fourth big man. That could be the catch-22 here: the Celtics need for a fourth big is as much as insurance for if one of the other guys gets hurt, which ideally you'd love a decent young or older vet. However, that veteran would have to be ok with basically seeing very minimal minutes when everyone is healthy which potentially many of those guys in that top group may not be.
I think Nesterovic might be the best bet in there to be ok with a flexible role, but if KG gets hurt then Sheed moves in as a starter and you have no back-up 4 unless Scal stays. A 4th big who can play 4-5 like Joe Smith would be a better choice likely, but I'm not sure Smith, Wilcox, or Frye are going to take vet min deals to come here and not play. Their strategy is best served to go someplace, anyplace, where they can play bigger minutes and show that they deserve a better next contract.
I think at some point they'll be a trade of TA, Scal, Giddens, and perhaps Pruitt (with money and future picks in need be) to a team looking to shed some future salary that fill in some of these more minimal roles (assuming the Cs get a 3rd win in free agency as well like Parker or Hill) like the 4th big, 4th wing, and back-up point guard. They'll be a vet min signing or two, but it may be from the "less good options" (with Robert Swift the most likely candidate) unless the Cs get a PF in trade as a 4th or 5th guy and maybe Nesterovic comes as well. I think a TA, Scal, Giddens, and Pruitt trade to NY for Dooling, Jarvis Hayes, and Sean Williams makes a lot of sense for both teams with NJ clearly giving the season away and wanting as much cap rooms as possible for next year.