I know that the Personal Quarters tickets give you extra rooms where you can place stuff, but I was wondering if there was a way to just increase the Placement Points for the Mini-Room. I actually like the cozy feel of that tiny room.

No, there is no way to increase the placement points of the mini-room.

The miniroom is set in stone and can't be changed. You have to get premium or a 3 day room pass to increase the placement points you have. Even if you lose access to the other rooms with more points, your decorations will be retained for next time you gain access, so you never lose them.