I just bought my first house in July for a permanent residence. 

Or a buyout refinance between the construction phase and the permanent financing phase. 

You will likely have PMI regardless so just make sure its in your cash flow calculations, and do the math for when you'd hit the 80% LTV mark, you should appreciate by that time and can always refi if you really wanted out of the "permanent" PMI of the FHA.

I was wondering if anyone has any lender recommendations for permanent/long term rental purchases.

You can also reach out to hard money lenders for some "permanent" capital solutions which will be cheaper than typical hard money rates but more expensive than bank financing. 

HOWEVER, the way this loan product is setup is that both loans (construction and permanent loan) are closed on the front end meaning I sign all closing documents.

It can also be transitioned into a long term permanent rental as well down the road or within the same year you purchased. 

Most of the RVs are permanently parked there.   

Don't assume that you've got their business permanently, or that they don't know other agents, haven't been approached by other agents, or that they wouldn't consider hiring another agent. 

Amy there is some language that states "All renovations must also be permanently attached to the property and add value to it.