He said that the door was to be closed

Note that in analyses of

"Close the door!"

as non-alethic, Grice still does consider (as I do) that there is a 'dictive' formulation which is very proper:

Utterer said that the door was to be closed.

While 'assert' and 'state' are NOT in order, 'say' and even 'saying that' ARE in order when dealing with so-called 'non-alethic' utterances.

And so on.

(He specifies this best in WoW:VI as I recall -- first sections on the form of the definienda).