Woody,
I've been shooting the MkIII series for years and have never felt the need to disassemble them to clean them.
We (me and my sons) usually shoot between 500 and 1000 rounds an outing and what I do is use one of the synthetic safe (I use Birchwood Casey) aerosol sprays. I lock the bolt back and thoroughly spray the gunk out of it, let it air dry (takes only a minute to be completely dry), then lightly lube the bolt with CLP and apply a drop or two with a needle applicator to the trigger control parts.
I then use an Otis cleaning cable and drag a patch with Hoppes through the bore a couple of times (breech to muzzle) and I'm done till the next shoot.
Disassembling them is tricky at first but once you've done it a time or two it's no big deal. What trips up most people is reseating the hammer strut with the mainspring cup, along with dealing with the annoying mag safety (empty mag inserted) to reposition the hammer to the rear to reinsert the bolt, then forward again to seat the mainspring housing.
That said, I can't remember the last time I disassembled it for a cleaning, seeing no need to with modern aerosol spray cleaners.