First, a $400K property that generates $3500 in gross income is a crummy deal. That's going to lose money.
Assuming you have a good enough deal to be interesting, you would have two roles in this deal. One is as the syndicator which is the person who puts together a deal. The second is as the PM.
A syndicator does often get paid some management fee for running the deal. A property manager gets paid a PM fee, which is on the order of 5-10% of the collected rents (lower percentage for more units). And perhaps a fee for filling vacancies.
As the PM, it might be reasonable that you would live in one unit in lieu of getting paid. But that would have to be one unit out of about 10, not one out of two or even four.
If you don't bring cash to the table, IMHO, you do not get any equity in the project. The investors own 100% of the project and get 100% of the returns, split up according to their ownership. As the syndicator, you might be able to get paid some management fee for running the deal. This is going to be fairly small, though I have one investment where this fee plus the PM fees are the only money anyone is making. All of us investors are getting nothing because the project is unprofitable.
I am dying to move out of my mom's house but refuse to rent! And I cannot afford to buy anything right now. Grin
Sorry, here I have a real issue. It costs SOMETHING to have your own place. Whether you pay rent on an living place or pay rent on the money to "buy" a place to live, you're paying rent. There are many locations in the US where it is cheaper to rent than to buy. I don't know about your location. But its as simple as comparing prices to rent. If the monthly rent is under about 1% of the purchase price, its cheaper to rent. If monthly rents are more than about 1.5% of the purchase price, its cheaper to buy. The exact numbers depend on the rent, higher rent and that second percentage can be lower. In between and its a toss up.
What you're doing is proposing a complex scheme that lets you "not pay rent" by taking your PM and syndicator pay in the form of a living space. Get past the "refuse to rent" hurdle. Because in what you're proposing you are very much renting. Separate earning the money (by being a PM, a syndicator, or some other means) from spending it on living quarters and you will have many more options on both counts. By building yourself this mental "refuse to rent" hurdle, you're hiding the rent inside this complex, and probably unworkable, arrangement.