ATF isn't a cleaner, it's the same base oils as engine oil, just with far less detergent, because it doesn't have to deal with combustion byproducts.
Since you have access down the front of the pan with the timing cover off, using something like B12 or a solvent with the drain plug out to wash off the timing cover area and see what comes out of the pan might be an idea. You could also soak the pickup in B12 if you put the plug back in for a bit. You could do this until it runs clean.
Then, after you button it back up, follow
@RDY4WAR's plan.
You don't want solvent circulating through that engine, it's going to break off large chunks of stuff that will likely cause damage, but I don't see a problem cleaning off visible areas and flushing the pan with some.