So the gist of it is they think the system that disables 4 of the 8 cylinders is malfunctioning and causing the miss and the noise? Probably a good next step would be to have a compression test done on the engine when cold and missing and warmed up and behaving and see what the numbers are. Since MDS works in part by disabling the valves on 4 of the cylinders, a compression test that is poor would indicate a valve problem, while one that is consistent both cold and warm (in theory) would indicate a problem with the MDS engaging on that cylinder when it shouldn’t. You say the engine gets quiet when the oil pressure drops–can you tell me what the oil pressure is when the problem is occurring and what it is when it goes away? Let me know if you need explained how to get to the readout for the oil pressure on the “EVIC” (the information display)
Hemis are notorious for a lifter tick, but typically it doesn’t affect the operation of the engine. They are not known for having head gasket problems, but of course anything is possible.
It may be worth getting a second opinion from another dealer or shop familiar with the hemi. But if the roller tappet that disables the MDS is malfunctioning, the price you were quoted doesn’t sound unreasonable to repair it.