I did a little searching and found a similar cover, a 343 precancel on a Marshall Field cover, in an article that Mel Getlan wrote for The United States Specialist about Schermack and Mailometer users in August of 2017.
Marshall Field was one of the earliest Schermack users and at one time had 7 of their affixing machines.
You may need a Chicago specialist to get any kind of a definitive answer.
Since it is a Marshall Field mailing, yes, one would expect some covers should still be around. And with Marshall Field in mind, would the precan type really be that scarce? It's still a good cover in any case.
I have posted it on the Frajola site. Had a little more discussion there, still hoping for a couple more members to chime in. I do know one Chicago specialist that frequents it. I'll contact him and see if he has any info.
Update: My contact is not aware of any. We both were able to locate #343 Schermacks with Chicago precancel on Marshall Field covers.