What's the easiest process for cutting bathroom flooring tiles to fit complex door trim?
I would cut the bottom of the trim so the tile can slide underneath. Then you only need to approximate the shape of the tile, but you don't have to worry about perfect edges.

I've used the Dremel Multi-Max with the 3/4" flush cut blade to cut base trim and door jambs so I could slide hardwood flooring underneath. I borrowed a friend's and decided I needed to buy my own as soon as my next project came up.