Can Simulacrum make a (living) duplicate of a dead creature, by RAW?

This is for a fairly absurd situation in which a party member (the cleric) has died and neither of the others can resurrect him, but one of the surviving party members is a wizard that can cast simulacrum.

Another player’s idea was to cast simulacrum to create a simulacrum of the cleric (with “half the creature’s hit point maximum” – which seems independent of its current HP) and then have the simulacrum resurrect the cleric.

The description of simulacrum says:

You shape an illusory duplicate of one beast or humanoid that is within range for the entire casting time of the spell. […] It appears to be the same as the original, but it has half the creature’s hit point maximum and is formed without any equipment. Otherwise, the illusion uses all the statistics of the creature it duplicates.

Ultimately, it seems to be a question of whether creatures retain their type after they die (i.e. when they are a corpse).

A few of Crawford’s tweets have stated that a corpse is an object that is no longer a creature, suggesting that spells that target creatures would no longer work on corpses…

…but then spells like revivify explicitly describe the target as “a creature”:

You touch a creature that has died within the last minute. That creature returns to life with 1 hit point. This spell can’t return to life a creature that has died of old age, nor can it restore any missing body parts.

And spells like animate dead even suggest that creature type is retained:

Choose a pile of bones or a corpse of a Medium or Small humanoid within range.

As a result, my findings so far seem somewhat inconclusive and contradictory. The intent obviously seems to be that simulacrum is not intended to create a duplicate of a corpse (which seems pretty ridiculous), but I’m not sure whether it’d work at least by RAW.

By the rules as written, could simulacrum be used to create a living duplicate of a dead creature (a corpse)?