The frame crack creation is accelerated or even caused but a worn out recoil spring. Others work but cost lots more with very little increase in accuracy. Until the ammo shortages the least expensive, reliable, accurate Std cell ammo was CCI Standard Velocity. Some models of Hi Std guns show less susceptibility than others but a safe person only shoots Std Vel ammo in any Hi Std gun. Some Hi Std guns fed High or Hyper Velocity ammo eventually crack their frames. The only ammo these guns should use is Standard Velocity ammo. There is controversy about things like ammo and maintenance of all High Standard pistols but here is the common ground that most owners and collectors accept without question. You can lube the internals with a needle oiler at pivot points. Remove the grips and soak the receiver in gun solvent for a day or two then blow it out with high pressure air. If you remove the firing pin retaining pin with a punch and hammer you can clean out that cavity. Clean the slide and especially the breech face. Clean the barrel and breech face normally (and after every shooting session). Remove the barrel then move the slide off the frame towards the front. Unless the gun is horribly dirty with caked on hardened dirt then don't fully disassemble it.

The guns are very similar except for the lever/button take down differences. The instructions you where linked to are for the 101 (button takedown). The Supermatic (100 series) uses a lever to release the barrel from the frame whereas the later 101 series uses a small button. The Field king was one step up the ladder and came with an adjustable sight whereas your Sport King did not. And indeed the 'screw' you refer to is the seat for the elevation adjustment screw of the rear sight. I have a Field King Supermatic (100 series).

High standard sport king