The ice is freezing into a solid slab and will not drop into the bin

that could be one solution. I would look at how long the freeze cycle is lasting. The machine could be cycling off and on via bin stat. Average cycles from start of freeze cycle to start of freeze cycle is usually around 25 minutes or so. If it is taking longer than that, you may have to dig deeper. let me know. Don't overlook a leaking water valve.

Manitowac uses a plastic deflector which has a magnet located on the bottom. When the machine drops the ice the deflector opens breaking the circuit to the bin switch. This would indicate "Bin Full" condition. As the ice is used the deflector closes and the magnet comes in touch with the bin switch.
Most likely the bin switch needs replacement.

Check to see that the sensor that feels when the ice has built up adequately is swinging back to position after it harvests the first time. Check to be sure it's clean too.

lp

http://kitchen.manualsonline.com/manuals/mfg/franklin_chef/automatic_ice_makers.html
Start by checking out this manual on your machine. After that, get back to me and we can go from there.

The solenoid ( or dual valve ) is leaking and has to be replaced.

the problem is an unlevel icemaker to prove this do you see little droplets of water freezing from the icemaker or a remote possibilty is do you have to an R/O system and have you change the filter if unit has one.

The thickness probe should be approximatly 1/4 inch off of the evaporator.Sounds like you might have loose grids on the evaporator.turn the unit off and remove the curtain.use a flash light and inspect the grids.There should not be space in between the joints,if there is the ice will freeze behind the grids and not properly release when in harvest. Also gently pull at the grids,if they pull towards you or wiggle then they are separating. I have removed one of the grids and had the unit continue to run for sometime until the evaporator could be replaced.The plating being spotty causes release issues as well.Finally check the level of the machine,front to back and side to side.Not being level will also cause release problems

Something is holding your Ice Slab at the bottom from your description.
Some causes are
1 Dirty - scaled up evap, or just dirty w muddy covering,
2 the vacuum breaking holes are stopped up If it is making a sla whith the evaporator warm no ice take a flashlight and hold it where its shining to the back of the evap and look for the light on th cube forming slots next to the ones your shining the light into Upper corners of each hole must be open.
3 The slab is freezing uneve most like cause is a stopped up distributor tube at the top thats feeding the water down the evaporator.
4 On some models thay had a closer fitting water curtian (the cover in front of the slab) and the top of the sheet touched this and caused the slab to stay uprite and continue the "slide" forward.If your curtian is of the older style and has metal hooks on it with verticle slots n the curtian look at the slots and see if the slots are worn making the whole curtian slide down ward I have seen this several times.4B On some older models there is also a plactic coated wire diverter on the bottom infront of the evaporator. If the palstic coating is gone or the bottom or is not even, the slab could hang up there. 4C If you have the newer plastic pins make sure thay are seated in the mounting properly.
5 Nickel plating could be comming off (any copper color on the lower 1/3 of the evaporator?).
6 I have seen some of the horizontal plates them selves be loose and not in flush try pushing and pulling on them especially the ones at the bottom. ANy that are loose and comming out is your problem.
This lengthy extrapolation is by no means all of the possibilities but most of the common ones. If this helps you solve your proble please rate me accordingly. If it leads you to the correct and completed repair WOULDNT WE MAKE A TEAM?? And Good luck to you.

The bin control shuts it off when the ice bin is full. Without a bin control it should keep making ice and never stop.

If it's makes a good slab of ice the only reason it would melt would be a drain blockage holding water in the bottom of the unit or the water pan overflowing into the bin when it fills up. If you check the slab when it falls on the cutter and see a hollow looking spot in the middle you may have an evapoator leak. Yhis would require a service tech to repair.