Late June seems so far, but hopefully his condition will maintain itself until then.
I have heard of people force feeding their frogs and how it helped get them going on their own, but I'm not sure if it's necessary yet. If you do it for any reason, it should be so he produces a stool to be examined. If you do go this route, call to make sure they will accept it despite him not technically being a patient yet. Since you have a visit scheduled, I'm sure they would be understanding.
He looks deceptively good. Nice, clear eyes and, despite not eating, isn't too skinny yet.