Okay, the Exo is far too small for the leopard gecko I'm afraid. They want an absolute minimum of a 2ft x 1ft enclosure to maximise on floor space. They are not arboreal cretures so the height is not great for him. It'll be alright in the short term while you find something more suitable for him but he really needs something bigger
Even turning the Exo on it's side would help a little if you haven't done so already
How are you measuring your temperatures, and where from? They are too cool. Bump the heat up to 90-92*F and it may encourage him to eat. Being too cool he probably cannot digest his food properly and could contribute to the weight loss.
If he's having problems with his eyes I would remove the sand substrate and keep the environment sterile - kitchen towel is great for this as it can be changed easily and kept clean.
Good on you for finding a vet - I hope you can make an appointment soon and get to the bottom of this