We have three property managers, based on three areas/types of homes we own.
One deposits, like clockwork, on the last day of the month that the rent was received, so about 30 dd. It's OK after the first month, and I think it's fair that they protect themselves against clawbacks or repair costs (they don't have a reserve per property that they hold).
We had one that started off with the same scenario described in the OP, paying off around the 15 th for the PRIOR months rent, AND they held a reserve of $500 per property. These were our first PM and we didn't know yet to negotiate, and what an unpleasant surprise that it took a couple of months to see our first partial payment. When it came time for renewal, we were an important enough part of their portfolio that we renegotiated to get paid on the 15th the for the current month and to have a reserve of $250 per property.
The third, who we are getting rid of now, is a mom and pop that deals with our lower end properties. They actually pay out the earliest, and don't carry a reserve, but seem to require a phone call inquiry around the 6th/7th to check on which rents are paid, which notices need to be sent out, etc. We get paid around the 7th, with a second deposit later in the month for stragglers. I'm getting a little tired of having to micromanage, and pay for that priviledge, so getting ready to switch those properties to one of our other managers.
So, bottom line is, you will probably have to wait some, but the 6 week thing is something you don't necessarily need to accept, unless this PM is the only option in your neck of the woods.