1996 Chrysler LHS, stalls intermittently at slow down or stop.

Car starts and runs well, cold or hot, level or grade, plenty of power all instruments indicate normally, all ancilliaries operate normally, no check engine light. Intermittently the engine stalls when slowing down, straight ahead or turning or stopping. Immediate symptoms are that the oil pressure light illuminates, the tach drops to zero and of course no power or throttle response. The engine restarts without problems after a stall and runs with its normal smoothness. I believe that the problem is electrical or power-train computer related, since the same symptoms have been demonstrated with two different new, factory remanufactured, engines.

This problem has been happening for over two years. The car has been in and out of the local Chrysler main dealer's shop many times during that period. In every case the dealer reports no stalling on diagnostic drives, unable to reproduce the problem, no fault found, no error codes set. The car has just had a new factory re-manufactured engine fitted, within 62 miles on the new engine I have already experienced one incident of engine stall when stopping from low speed at a car park exit.

I'm not a lead footed or heavy handed driver, that's for fools, I adhere to Stirling Moss's dictum that the mark of the good driver is how smoothly he or she can drive while proceeding at a speed appropriate to weather, road, journey and traffic conditions.

I really like this car, it's the nicest US designed and built car that I have had in many decades of driving and I don;t want to part with it; but this unpredictable stalling is making me very uncomfortable in respect of safety in traffic. I'm very unhappy with the inability of the Chrysler main dealer to diagnose and fix the problem, even while I sympathise with his difficulties in locating an infrequent, intermittent problem. The vehicle has been very well maintained during its life and still looks like new, so the problem is not the result of neglect.
Any help that you may care to offer will be appreciated.