I’m doing something similar, but taking a very scenic route - so doing a lot of sight seeing along the way. I’m using the TBM which has proved to have the range and speed needed to make this enjoyable (I don’t want it to become a chore) and happily seems to be one of the more stable aircraft.
I use little nav map too, but in reality that isn’t needed. You can set up all the flight plans from the world map, specially if you are essentially using VFR, which I assume you are so you can sight see properly.
I’ve been keeping a bit of a blog going on these forums, so feel free to have a look here