If your CAT6 is down to 100 Mbps, check that all the conductors have been properly crimped into the connector -- or consider re-crimping. It's possible the building has shifted and damaged the fished cable, but it's more likely the problem is with the connector(s).

I confess, I've read this twice and I don't really get what's going on here; and I have both MoCA and Powerline going on in my house as well, so I'm like -- why not one of those?

This is how my apartment complex retrofitted all 300ish units with AT&T fiber. Fiber runs from your building's telecom room to a small hole they drilled above everyone's front door, then along baseboards and around door jambs until it reaches ~the center of the unit (concrete walls...) in the living room.

It is genuinely invisible until you get up close. You're far more likely to notice the spots where someone got sloppy with the glue in some corner than the fiber itself. With proper attention to detail during installation (and assuming you have white door jambs and baseboards) it would be basically invisible.