1994 Chrysler New Yorker auto transmission/downshifts by itself

The electrical part is because the transmission is computer-controlled. The first thing you need to do is have the diagnostic fault code(s) rear and recorded. That will tell you the circuit or system that needs further diagnosis or the unacceptable operating condition.

Also, most scanners will display the "clutch volume index", (CVI). That's a set of four numbers corresponding to the number of CCs of fluid it takes to apply each clutch pack. Based on those numbers, an experienced transmission mechanic can tell you the percentage of life left in each one. Based on the mileage, it's a good bet there is slippage taking place in one of them. That will set a gear ratio fault code.

You're correct that turning the ignition switch off, then restarting the engine gets it out of limp mode. An easier way to buy yourself some time is to accelerate a little harder than normal to delay an up-shift, then let off the gas to reduce the torque on the clutch packs so they don't slip during the gear change. Once they're locked up in the next higher gear, you can accelerate and do the same thing for the next gear.