Their manual sucks, but I would look at the Samsung BD-E6500 which is a slot load player that may work, and I would take a look at the BD-ES6000 which is a slot loading player that I am more skeptical about working.
None of their documentation talks about it, but their main web page still mentions 'wall mountable' designs.
Blu-Ray Players: Compare Reviews, Features, Connectivity & Prices | Samsung
But, I would go to a store and get hands on with some of the players and hold them sideways with a disc to see if they still work. No 'top loading' one will work, but the slot loaders may work.
Could always eBay it and pick up an older 7500 player.
Portable, car type, players will also all have some potential. Depends on how serious you are going to be about it.
EDIT: Check this one out...
Panasonic DMP-BBT01 - Smart Network 3D Blu-Ray Disc Player DMP-BBT01 - Overview
It can be mounted vertically, is slim, has a slot load design, and is a current model. Still, not really what you are after I realize, but it just isn't an often requested feature.
