So doing the math you're grossing at least 541,000 a year with 41 units at an average of 1,100 a month (which is low for the northside of Chicago). You want to pay someone $50k but you want to split that with someone else? On the one hand a PM will charge you 7-10 percent, right? But they will take care of all of that.
A maintenance guy who shovels sknow is not going to be able to do plumbing, electrical, and HVAC unless you're talking about changing the furnace filters and not much else. I have guys who might do what you seek for $20-25 an hour. At $20 an hour times 40 hours a week you're looking at $38,400 a year. A plumber or electrician won't work for that.
Although I don't recommend it if you have a free apartment that goes with the deal maybe that salary would work for a higher qualified person. Anyway, I do know guys who will maintain your building, cleaning, snow removal, light repairs, etc., on a per building/unit basis or per hour basis (I think).
What happens with guys like you who have that many units is they create a property management firm within their own management and do it for others as well. Maybe if you pool together with some other owners you can bring more resources to bear and start your own PM company.