What should be used to replace the black goo around the evaporator tubes where they come out of the case?
You can buy that stuff from places like Ames and others. It's like caulking on a tape, you wrap it and squish it.
I bought some from a RV dealer it is used a lot on them cost about 10.00 a foot and its around 2 inch wide. I probably still have some if you need it,.
I use a product called gum seal in the HVAC industry. Its rubber and ground up cork molded into stickey strips. works great for an application like yours.