The one MKIII that I owned was basically a Jam O Matic from that miserable
thing, someone does make and market a replacement plug in that doesn't move
at all and that ostensibly remedies that problem leaving only the other lawyer
inspired abomination, the magazine disconnector. I abandoned the entire
MKIII series as a bad idea and a solution to a problem no one asked for and
stuck with my MKIIs that are as solid as the Rock of Gibraltar in my experience.
You could ask around for a link to whoever makes the replacement piece, it might
be Tandemkross or Majestic Arms, both can be found by Googling, good luck.
Here is a link to the Tandemkross part in stainless, they also make a blued version
for the same cost depending on which you need.
https://www.tandemkross.com/LCI-Replacement-Insert--Stainless-Steel-for-Mark-III-and-2245-_p_62.html
On their website there is also a short very handy video on installing the replacement