Wanted to follow up on this because it was a bit of a pain in the neck trying to get this thing apart. Maybe some pics will save someone else some time.
The "gunk" on the screen was caught between the clear LCD bezel on the cover and a sticker-type screen protector glued to the outside of that. I must have spilled/splased/drizzled hot wort on it at one time and it was enough to loosen the glue and get behind it. It wasn't apparent until I got everything apart. I did away with the glued-on protector and instead cut a square off some cell phone screen protector film I had laying around. This should be enough to keep the plastic bezel from inadvertently getting scratched and will be easy enough to replace without dismantling everything.
There's an inner kettle and outer sleeve to the Foundry which comes apart. It's a slip-fit at the top to keep everything aligned. I had wort dried between that space which had basically glued things together. When I tried separating the two (to get to the screen) it didn't want to budge. I ended up putting a 1 gallon bucket under the kettle part and the pushing down on the Foundry handles which made it separate much easier.
The screen/controls are covered with 1/4" neoprene (wondered about putting a layer of this stuff all the way around the inside to insulate.. hmm). Four screws which attach the screen cover are under the neoprene. In my case, all the screws were installed at an angle and not straight into the boss. It must have been a Monday or Friday at the factory. Makes it a little confusing when your trying to remove them because there is neoprene stuck to everything and you can't see the angle of the screw head. I couldn't find a way of saving the neoprene as the entire thing is adhesive backed. After peeling it off with a plastic scraper, I used laquer thinner to clean up the leftovers. It was a mess. I picked up some neoprene off Amazon for $15.
The clear bezel for the screen is hot welded to the black cover with four plastic posts. This is where I noticed there were two layers to the screen. Luckily, I was able to cut through the hot weld with a razor knife. I probably didn't need to do this after realizing the outside cover on the screen was just glued on. I think I was assuming the entire bezel needed to be replaced.
After getting things put back together, I tried some silicone caulk around the bezel but caulk isn't my thing and I just made a mess of it. Cleaned it off and found this silicone putty type stuff on Amazon called "Sugru" and gave that a try instead. You can roll it into a small cylinder and pack it around the seams. You get a good 10 minutes of working time with it. It cures semi-soft. It's a 1-star appearance, but seems to seal OK. Supposed to be easily removed if I find a cleaner solution sometime.
All in all, It was about a six hour repair. Be sure to label all the wiring, especially for the heating element. Oh, some of the connectors on the bottom of the unit have adhesive of some kind dabbed onto them. Not sure if it's for tamper evidence or to keep things from wiggling loose over time. This has to come off. I just used a dab of silicone RTV when re-assembling.