route is nearly as short as possible. ... but 13.5k in a very nearly
max gross PA28-180... I dunno. Could be fine....
Going up to 13500, I'm legal for up to 30 minutes, but is it smart?

13.5 I think is the ceiling and that is at standard temp/pressure.
Have you checked out the temperatures at that altitude. They
very well might be above that temperature so you might only be able to
ge up to 12000 MSL.

Gerald