realtors don't manage the property, they just list them and show them. The listing agent represents either the owner or the owner's property manager. You can get your own realtor to show you places if you want to; I don't think it costs you anything.

You might be appealing to an owner because it sounds like your income is very reliable. If the rest of your application shows well, I bet many owners/managers would be fine with the income.

Also, there are a bunch of posts here you can find via search of people recommending various property management companies.