These properties typically do not have rent growth that keeps up with inflation.  

I think hard money lender to take this risk cannot legally charge appropriately which means the law is working against you (the law meant to protect owner occupied owners from unfair loans).I agree with @Jay Hinrichs that your best option likely is to sell on the mls.  

That does not mean you are getting the best one unfortunately.

We aren't the cheapest place but we are affordable for the size and I want to keep it that way.

This almost always means they are a land lord or the property is currently vacant and likely to sell soon.

I'd keep the rental and by no means refinance it to take cash out. 

For the second, by "trying" I don't mean that we're struggling to do that but I see why it comes off that way.

I mean come on!

For me “time in” the real estate market means “time out” of the stock market.Any advice on how to reconcile or justify that?   

Otherwise, I don't partake in keeping up with the Jones's.