I would:
Add ARX
drive for 1k miles
Drain
Remove pan and clean
Remove Filter screen assembly
REPLACE FILTER SCREEN ASSEMBLY,O-RING, (and new pan gasket if used)
refill with ATF
I would replace the filter screen since the mesh will probably be coated with friction disk resin, which appears to just make the screen caramel colored, but does reduce flow. This normally wouldn't be an issue, but you may continue to have solids break free and get trapped at the filter.
Whenever cleaning out a trans you run the risk of debris cloging the valve assembly (requiring a power backflush or disassembly) but this is rare in my experience, and from 1st hand accounts of others.
Saturns had spin off trans filters (awesome idea), and most Asian cars dont use a pan, just a drain plug and fill plug.
In cars without a pan which can be removed, I would ARX, drain, fill with cheap ATF, drive for another 1k miles, drain, and refill with quality ATF. All this will do is remove a few more solids from the trans that could potentially add restriction to the uncleanable, permanent, pick up screen.
Just by having new fluid in there, you will probably notice an improvement in shift quality.