I think your 93 Regal transmission is electronically shifted using solenoids inside the transmission,, if this problem your having occurred suddenly I would suspect one of the solenoids is acting up.
The solenoid has a copper wound coil with a metal plunger, similar to what you would find on a washing machine water solenoid but only smaller if the insulation on the copper is breaking down this would cause a short also if some grit found its way between the metal plunger and the casing its housed in this would cause intermittent operation of the plunger.
I have not rebuilt an automatic transmission in over 25 years to which most were mechanically sifting with the exception of the Edsel and some Chrysler's with the push button shifter. When I last spoke with Norm the guy I apprenticed under and now owns his own trans shop told me they change the solenoids on every rebuild never taking a chance reusing the old.
Our shop never practiced this bit of deceit only because Norm wouldn’t play the game, some shops will save broken bits from a trashed transmission then show this pile of garbage to a customer claiming his/her transmission needs a complete overhaul immediately in order to avoid an imminent break down.
If your capable of pulling a transmission you can easily rebuild it, plenty of youtube instruction available for the most popular models. When you purchase your rebuilt kit get the MASTER, and always install a shift kit.
Transmissions are made to shift with a soft shift, I call it the granny shift, this soft shift creates unwanted heat leading to premature transmission failure the shift kit firms up the shift allowing the clutch packs to engage quicker with less friction. On the turbo 400 one performance trick was to drill a few holes in the clutch drum now instead of the oil being forced out and over the edge of the drum centrifugal force would assist the oil to escape from inside the drum.
Oil coolers and shift kits are the best prevention.
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