Yeah, that's a good idea. The oil pickup bolts to the oil pump, which is mounted on the front of the crank, behind everything else. If you had the front cover off, you might be able to unbolt the pickup tube, I can't remember. And then flush it with solvents, air, etc. Some debris might still get caught in the covered portion of the pickup tube's pickup though. But as long as it isn't enough to clog the pickup area, you might be ok.
I don't think you can remove the entire pickup without unbolting it with the oil pan off. There is a bolt, right near where the dipstick tube ends up in the block, that holds the pickup up in the rear.
You could change the oil for something as thin as possible, 5w20 or preferably less, run the engine for a minute, shut it off, let the oil drain out for 5 minutes (backflushing the pickup), and repeat over and over. Change the oil a couple times in short intervals, like every couple days maybe.
The problem is that the oil pump uses 2 gears that are close fit, to compress the oil, and from there it goes thru the filter. So the pump gets unfiltered oil. If a big chunk gets in there, it could cause pump gear damage.
Since the alternative in a 4wd is grim, I would try it. Perhaps with a mechanical oil pressure gauge hooked up, for constant viewing. If the pump does break, you would be able to catch that right away in this process. At that point, you would still be in for pulling the pan, front cover, etc. But if you get away with it, you're only into the front cover.
If you tried that, I would think about pouring a solvent like mineral spirits into the oil pan from the front/oil pump area. And also backflushing the pump pickup with solvent as well. The idea is you want to be able to wash all those plastic pieces out of the oil pan via the drain hole. I'm talking about a gallon of mineral spirits here.
Then once you fired it back up, any remaining mineral spirits would be mixed in with the oil. A couple quick oil changes would help to catch any plastic, as well as get rid of the solvent-thinned oil. Im actually not that worried about the bearings, as I've seen mineral spirits poured into engines and used as a motor flush, and the motor was just fine. Short term, with a quick oil change after the initial oil change, that doesn't seem like a problem to me.
If you want to send me your email address, I've got pictures of a Cobra 4v pump, pickup, etc with the oil pan removed.