Oh that is so true. I have to agree with your thoughts about MC not dying, I initially thought they were dead because it could make the reason why Liotte was so frantic in wanting MC to come back to them, but we can attribute that madness to the direct result of a constant time loop practically traumatizing Liotte into losing whatever remnants of MC there is.
I think that Liotte holds romantic intentions towards MC before even the loop occurred due to the "stalking" items we find in the backstage. But if we go with the missing scenario, Liotte might be doing an intense investigation trying to find MC which can be written of ass stalking and harassment (especially if Ivan put those things into focus during a period where Liotte was becoming unstable to MC). Another thing I was curious about is if Liotte is only trapped in a TV show, if he wasn't and he was just trapped into a TV would that mean the CCTV footage of MC was him stalking MC? But that wouldn't make much sense because the time loop only happens on one day and the pictures of MC must have been done over a few days and so on so this must have been done before the time loop occurred.
Also I get the comparison between Liotte towards Furina, Scaramouche, and Lyney~! Though I have to say Liotte's design and general coy attitude leans more to Lyney instead of Furina's boisterous show business attitude while Scaramouche's trauma of abandonment and bouts of mood disruptions mirror how Liotte's mental state deteriorates the longer we converse with him.