You are going to have to leave him with someone, repeatedly, and allow him to cry it out. If he gets so hysterical he passes out, then that may just be how it needs to be. Certainly do not wait until you are actively job hunting in order to find someone to care for him in your absence. I would make sure you are leaving him quickly without a bunch of fanfare and do not play into any drama or manufacture it due to your own feelings in this situation. I am surprised at how many parents I have observed (dropping off at school, parties, play dates) who clearly telegraph their own issues onto their child and take the drama up several notches. Sometimes they don't realize it, sometimes they do-but either way, be cognizant of it.
Mothers morning out is not your solution if he can't even allow you to be at a funeral for heaven sake. You are going to have to hire a 1:1 caregiver and walk out the door and not return for at least two hours. How are you going to go on interviews and be on time for work if he is throwing a fit because you are gone? Deal with it now, not in a month, because you are not doing him any favors by extending this situation.
I hope this is a built in PSA for parents who never take time for themselves to have dates with their spouse, alone time or whatever--and have their kids with them 24/7. Things DO happen where you need to leave them and they need to know that it is okay when you are away and that you will return.