The problem you have is one the contract can be lost, management companies always look for better deals.
The other problem is will the management company accept the new guy, I do a lot of apartments myself and they are very specific that only me or my staff clean them, I cannot sub contract or sell the work on.
If they agree the next problem is the price, nobody is going to pay 5 times the rate if it's going to take them a couple of years just to get there money back.
The best solution would be to sub contract it out and take a small cut.