I have a 02 doing the same thing. For a while it was just longer starts. Now I can't get it started. It doesn't have enough oil pressure to start. I unplugged the the sensor and it still will not start. I am sure I have an injector o-ring leaking. So I am going to pull all of them and...
The oil cooler in a way is a filter. A remote filter is finer than the oil cooler and only stops what goes thru the oil cooler anyway. Everything coming out of the block has to go thru the oil cooler first. But they still help.
I am running the 6637 filter. The problem with it is your intake temperature will go thru the roof pulling hard going down the road. That kills horsepower. Never draw under hood air.