How long is the drip down time on the case. also LLSV could be getting stuck open if so open up vlv and check out. as someone mentioned befor check to make sure you are not flooding the coil . if the store has no Dehumidification then they might want to think about installing it. all this will do is help.
An oversized liquid line solenoid is a bad thing...it may not always close all the way. Be sure your LLS is properly sized.
Cases icing up usually means loss of refrigeration capacity. Even with scheduled defrosts, an air defrost needs to be off 4-6 hours in a day to keep clear. Check your charge, tx valve, clean condenser, clean evaporator, check fans, everything. Make sure the compressor is pumping, see if it draws a vacuum with suction valve closed. I suspect you'll find something wrong in the refrigeration cycle.
I ran into an odd one this summer. One section of a tyler case would ice up, the other sections not. This is the type that every 4 feet has an evap. Ended up that the case was not level, and on defrost the fan cabinet would have water sitting in the bottom and wouldn't run clear. The water was blown back onto the cold coil, making a nice impermeable layer of ice on the bottom.