I wonder in these situations, if you can at least get information in by writing signs (obviously only when the child can read?) They may not be able to organize themselves enough to write back, but it might be worth a try to let them know that you're there to help, and that you will figure it out.
I know with my son, during a meltdown he's unable to communicate even if he has speech - he can call us names or scream angry threats, but he can't let us know what's going on. We usually send him to his room to calm down on his own.
Afterwards, we have succeeded in "discussing" things via a written conversation. The more often we successfully communicate - even if there's a delay to wait for the meltdown - the fewer, shorter, and less intense the meltdowns are for us.