questions - Must (Past Obligation Interrogative) "Must you have eaten all the food?"

Is the question "Must you have eaten all the food" correct when used in the past obligatory sense?

The best examples I can find are quite ambiguous.

"Must He have been less than perfectly kind to one of His creatures? I do not think it can reasonably be argued that in such a case God must have wronged one of His creatures."
-Kopelman, ‎L.M. and Moskop, J.C.; Ethics and Mental Retardation, 1984 [pg. 130]

If you change the question to read as follows it seems to share a similar intent:

"Did He have to be less than perfectly kind to one of His creatures? I do not think it can reasonably be argued that in such a case God must have wronged one of His creatures."

I am looking for solid references or consensus as to why "much" can't be used in the past deontic sense.