So I talked to a very experienced refrigerator repair guy and sent him the photos and explained what I was seeing. He said it's most likely the compressor getting weak and not building enough high side pressure, or it's a slow freon leak, which he said is pretty unlikely from his field experience. Probably so, since I have also noticed that I had to set the freezer temp setting a bit colder on the thermostat over the last 6 months to keep things frozen.
Cost of putting in a new compressor would be the same as just buying a new lower end fridge ($1000~$1500). He said the new refrigerators today are basically "disposable" if they have any major repair work needed. Plus he said a lot of the new fridges today come with a measly warranty, like only 1 year when before they were around 3 year warranties.
The reason it was cooling better with the ice block on the inlet side of the evaporator is because that ice ball helped as a cooling source, and it also allowed the expanding freon to cool the evaporator farther down the coils which helped the cooling efficiency by adding cold surface area.
It's been ~3 days since I melted the ice ball off the evaporator, and the fridge is slowly gaining some cooling performance (enough that the ice maker now works some times), probably because another ice ball is forming.
So guess it's time to go new fridge shopping. The guy I talked to said the two top best brands these days are Kitchen Aid and Whirlpool. Found a Whirlpool at Lowe's on close-out for $839 (was ~$1200), should probably just go buy it.
Some of these high end refrigerators are over $5000 ... crazy!