I've got this exact same issue. Used the dye twice and I suspect the same, Evap unit. I'm thinking of tearing the dash apart and doing the dye to see if I can find it. Not looking like a fun job to take the dash apart that far, but summer is around the corner here in TX. If I can get to it in May, I'll let you know what I find.
My timing will be similar to yours. Might be tearing mine apart about the same time as you. June is triple digits for us, and having cold air blowing on you while on the trail is nice. You might as well replace the heater core while you're in there. That is my plan at least, but I have a lot more miles on my rig than you do, so a toss up for you me thinks.