MAVS NEWS:

[F Gump]

“they won’t take themselves to just under the tax and hope to stay under it.

This feels clear to me.  They WON’T do it.  I don’t know what else to say here.  Won’t seems pretty unambiguous.
There wasn’t a qualifier.  Using the full remaining MLE amount takes them right up to the line, so they won’t put themselves in that position again since they “learned” that lesson just a couple of seasons ago..

Thank you for the explanation. Yes, I know what "won't" means, but what threw me off was the remainder of the sentence, with the "and", that I took to be saying "they won't ____ and (they won't) hope to stay under it." The challenges of online communication. Onward.

One small side point that you might want to add to your thinking:
While the g'tee dates on Cisse serve to lessen the cap hit cost of waiving him at certain points, I think those dates are probably meaningless, because Cisse would have a very good chance to be claimed on waivers if he was cut. A waiver claim would only commit the claiming team to a one-year minimum, and they couldn't save any money by letting him clear waivers and then signing him. The relevance is that it would erase the entire cap hit from Mavs cap.

That possible cap hit was never going to be all that much anyhow, as you note, so this wouldn't change the viability of anything, but it might help us to consider that those g'tee dates are possibly irrelevant to the Mavs.