The first thing I would be looking at is to confirm/deny one or more almost-plugged catalytic converters. That can explain the poor performance effects as described. And the excessive backpressure in the exhaust system can be popping off the DPFE hose. But test to verify.

Can use a vacuum gauge to check intake manifold vacuum to check for exhaust system plugging - engine vac will be reasonable or close to reasonable at idle, but will drop and stay low after the engine is revved under load and accelerator held steady (hold brakes and load engine up in drive), or put a long enough hose on the vac gauge to route hose through window and take it for a drive. Vac will drop momentarily when the throttle is opened, but should increase again if OK. With plugged, will stay low.

Another way is to temporarily disconnect exhaust pipe(s) ahead of cats and see how it does loading it up with brake torque while stationary. Some have pulled out the forward oxygen sensors to create an escape path for exhaust to check.

For me, I would use a vac gauge, and if it looks bad, then disconnect exhaust pipe from exhaust manifolds, just need to back the pipes off far enough to leave an airspace for exhaust to exit, for the final verify that indeed cats are plugged. Plugged cats can break up too, and pieces can move downstream into muffler.

When disconnected, exhaust pieces can be tested by using a big shop vac on the air exit mode - put shop vac hose with air blowing out into the piece, use a wet rag to help make a seal. All mufflers, pipes, cats, should be very free-flowing.

We used a vacuum gauge to verify plugged exhaust system on a V6 FWD car. And then disconnected the exhaust pipe from manifold, could only back it off 3/4" or so, but that was plenty. We brake-torqued it then, the vacuum was now decent, and the engine acted properly. Since it was FWD, there was no exhaust pipe over a rear axle, so we disconnected the electrical connector on the oxygen sensor, and disconnected all of the exhaust hangers, and dropped the whole exhaust system onto the floor. Then dragged it out from underneath, and started disconnecting. Testing the cat with the shop vac in air-output confirmed the cat was almost totally plugged. We blew some pieces out of the pipes, and reverse-airflowed the muffler and resonator while tipping them every which way to be sure nothing was caught inside. Then putting on a new cat solved the problem. This was on a >>100k mile car.

EDIT: On the car we fixed, looking at it with a OBDII scanner showed nothing constantly wrong. There were some intermittent codes here and there that would be different each time, but no codes that had anything to do with oxygen sensors. It was a stealth problem, as far as OBDII was concerned. It took my old-school knowledge to approach it differently. A few minutes with a vacuum gauge, and a quick test drive for a block with the vac gauge in the car nailed it. The exhaust pipe disconnect was icing on the cake, we felt confident then ordering up a new cat assembly.

ts the cougar just different body & the added 4x4 but same ****