That screen is indeed bolted to the valve body and can be accessed by removing the pan. Not too much to it, tho. Transmissions don't generate a lot of sludge and the screen doesn't trap anything - it just keeps the big pieces from getting into the pump. From there fluid flow eventually puts it thru the spin on filter. The point is that the magnet in the bottom of the pan catches most of the iron filings, and the rest floats around in the pan.
Since there isn't any carbon buildup or junk from the intake system getting flushed past the rings like the engine, the trans stays pretty clean. Dexron being 60% detergent keeps a lot of stuff in suspension and won't let it accumulate.
There is a TSB on delayed shifting on the Phase II 4EAT and it was an engineering choice to improve mileage, It's not a tightly valved transmission that instantly responds to control, more like a polite "I'm getting to it." and it's noticeable if you switch from a Detroit make back and forth. Same for downshifting under power - the trans computer gets into economy mode and it will take a two-count getting around to it. You have to drive it in third for awhile to improve the downshift, or do it manually with a poke at the accelerator pedal. All known symptoms of it being Subaru, not so much a symptom of it being a malfunction.
The line pressure has something to do with it, when the solenoid or dropping resistor fail, you can count on it shifting a lot harder and with no finesse. That is another way to test for the source of the problem - disconnect the resistor and you should experience it going to limp mode, hard early shifts, stuck in 2 or 3rd, with a constantly flashing AT TEMP light and throw a P0748 code, at least in a 99. If the trans mechanically fails, none of the sensors "see" it and you get limp mode with no codes.
No need to ask how I know. Anyway, if your lag is more than normal, it might be hard to assess over the internet. You could add a can of transmission cleaner to see if it sharpens up the shifting action, cheap solution first. If it does nothing, then varnish or sludge isn't likely the culprit.
I have three Subaru AWD vehicles in the yard, 98,99,01, they all seem to shift the same, just a bit of lag and certainly less sharp than a 03 Caravan. It has the least mileage, which is another factor - transmissions with a lot of miles just run a bit softer and less crisp. The newer one I've installed seems to have it a little better than the older with 220k on it when it failed.