How do I shut down the fuel pump to be able to change the fuel filter on a 1987 Chrysler New Yorker?

Fuel filter is definitely not the problem. Other than on diesel trucks, you will never solve a running problem on a Chrysler product by replacing the fuel filter.

The automatic shutdown relay either runs the fuel pump directly or through another fuel pump relay, depending on the year and model. That relay only turns on for one second after turning on the ignition switch, (you'll hear the hum of the pump for that one second), and it turns on again when the engine is rotating, (cranking or running).

If you follow the service manual directions for bleeding down the fuel pressure, it involves powering the injector to dump the fuel into the intake manifold. Mechanics don't have that kind of time to waste and they don't want to have to charge you for that step. They just disconnect the filter and let the few tablespoons of gas spray out. It's all over before you know it.

This sounds like how MAP sensors used to fail. The signal voltage is very precise and it doesn't have to be off by much to affect engine performance. Even though that voltage can be wrong, as long as it's between 0.5 and 4.5 volts no diagnostic fault code will be set. The Engine Computer will command fuel metering based on those incorrect voltages resulting in poor performance.

Be aware that if you try to find a used MAP sensor in a salvage yard, they are different for cars with turbos. Regular MAP sensors measure barometric pressure and intake manifold vacuum. With a turbo, those sensors have to also measure manifold pressure.

There was a recall related to the MAP sensors too. People didn't have a problem if they finished out the dollar after the gas pump kicked off or if they stuffed the gas tank, then drove 15 - 20 miles. It was when the pump kicked off, then they squeezed and squeezed to get more gas in, then parked it on a hot day. As the fumes expanded in the tank they worked their way through the evaporative emissions recovery hose to the charcoal canister, then up to the vacuum hoses. It's there the fumes would deteriorate the protective jelly in the MAP sensor.

The vacuum hose going to the MAP sensor, which sits near the right strut tower, is pretty long, and the fumes would condense and the resulting liquid dampened the vacuum signal. The fix in the recall was to cut both ends of that hose near its ends, install a pair of tees, and run a second hose in parallel to the original one. That doesn't seem logical but it worked. The theory was the air in the hoses would circulate and dry out the vapors. If you see a tee in the hose near the MAP sensor, that recall was done already.

Another potential cause of your problem is a jumped timing belt. One tooth off will be barely noticeable at highway speeds but it has a big effect at low speeds. Check the ignition timing. If it is excessively retarded that's because the distributor is driven off a sprocket run by the timing belt. Even if the ignition timing is right, it can be the belt just jumped on the camshaft sprocket.