You should be able to beat the existing rate even. 

We recommend you get management contracts from several PMCs and compare the services they cover and, more importantly, what they each DO NOT cover.

We don’t know any PMCs to recommend in the area mentioned, but since selecting the wrong PMC is usually more harmful than selecting a bad tenant, you might want to read our series about “How to Screen a PMC Better than a Tenant”:https://www.biggerpockets.com/member-blogs/3094/91877-how-to-screen-a-pmc-better-than-a-tenant-part-1-services-and-processesWe recommend you get management contracts from several PMCs and compare the services they cover and, more importantly, what they each DO NOT cover.

Any semi-intelligent agent is going to do the math and want to cover their expenses.

Unlike refinancing, which involves taking out a new loan, recasting keeps your existing loan terms—including your interest rate and loan duration—intact.

I'm not sure if the program is still going on, but has definitely revitalized a lot of the area when it was once destined to follow the way of other older cities that are aging out of existence both in terms of people and property. 

For a long-term rental, would a small multifamily in Raleigh be necessary to break even and cover the mortgage compared to a SFH?

With this route you can purchase a turn key property and expect to lease the property immediately or purchase an existing rental from an investor that doesn't require rehab and has strong numbers. 

The denominator in the calculation is your capital/equity and with no debt the return on your existing equity is low.

Have you called the housing authority that covers this property to confirm the max rent based on the # of beds?