FYI the Celtics literally CAN"T take on Batum, after using the full MLE they are hard capped at a number where they can't absorb Batum. And at 27 million Batum is fairly difficult to move.
The easiest solution is CHA sending out Zeller who makes 14 million, but I doubt the C's want him because taking back his salary cuts into the TPE you can generate and ideally you'd want to make one big enough for Beal (we can dream). One possible solution is sending Theis to CHA to replace Zeller and Zeller to a third team. That clears 9 million in salary which is enough. In this case the Celtics "pay" for the TPE by using Theis, CHA sends some picks to a third team to absorb Zeller. Here's an example, you can quibble with the draft picks each team gives up.
BOS
Out: Hayward (S&T), Theis
IN: TPE (33-37 million depending on Hayward contract)
CHA
Out: Zeller, draft pick(s)
IN: Hayward (S&T), Theis
NYK
Out: Nothing
IN: Zeller, draft pick(s)
Another possibility is OKC, who will have a trade exception big enough to absorb Zeller. This could be what the hold up is, waiting for OKC to sequence its moves so that it generates the TPE it needs to absorb Zeller or Batum.
I know people won't like trading Theis and if you think he's worth more than just getting a huge TPE then that's fair, but I think TT basically takes his role. Robert Williams then gets a shot at real minutes, and you can pick up another center with the BAE or for the min.