88 Chrysler New Yorker stalling issues

Recheck those codes. There is no 37, and 42 is related to the automatic shutdown relay. If the problem listed really occurred, the engine wouldn't run. The first code is typically 12 which just means the ignition switch was turned off. 55 is "end of message". Both 12 and 55 can be disregarded.

All of the parts you replaced so far won't cause that problem. One thing you might consider is the pickup screen in the fuel tank, although I suspect you would have seen if it was plugged with mud when you replaced the pump. It can collapse too after driving for a few miles and block the pickup tube. If you installed a pump inside the pump housing, you would have reused the screen. If you bought a pump from the dealer, (or some aftermarket pumps), they come with the entire housing and pickup screen already. I had the same problem you described with my '88 Grand Caravan a few years ago. The clue is the engine will actually run better when you accelerate, and it will stall when the pump has to move the largest volume of fuel, ... Which is during coasting. Once I figured out my problem and the reason it acted the way it did, a test became apparent. When the problem occurs, disconnect the vacuum hose from the fuel pressure regulator and plug it, then see if the engine runs better. You can expect a lot of black smoke from the tail pipe from running too rich, but it shouldn't starve for fuel. This seems to act up after the engine is well warmed up, and tends to run fairly well for the first 10 - 15 miles.

I had another intermittent bogging / dieing problem that I chased for eleven months until it finally died completely last fall. Every single symptom acted EXACTLY like a bad accelerator pump in a carburetor, except it got much worse on hot days. It turned out to be a shorting ignition coil. The only way I was able to find it was to wait until it died and wouldn't restart. (I also have the 3.0L). No more stalling and a little better fuel mileage since I installed a used coil.