Indeed, if McConnell were in perfect health and a Democratic senator were in this position, McConnell would be leading the charge to ensure they resigned.

No, McConnell wouldn't "ensure someone resigned", he'd use some procedural trick to remove them from office and have a Republican of his choosing fill the seat. And, he'd do it even if he knew full well that the person was alive, conscious, fully in possession of their faculties, but somehow unable to defend against that kind of a dirty trick.

The governor of Kentucky should simply replace McConnell, and if it turns out that McConnell is, in fact, up to continuing to serve in the senate, he can fight to get his seat back.