"The 1099-R was issued to the decedent's trust, and the 1041 input screen does not have a rollover option!  Does the fact that the distribution check was addressed to the decedent's trust make it impossible to do this?"

Yes, that's yet another detail that matters.

Somewhere on this forum we discussed that the Trust or Estate can protect an IRA account for inheritance by requesting that the disbursements go into account(s) for the beneficiaries set up as inherited IRA accounts.

However, that doesn't seem to have happened here. It seems you have a plain distribution.