I don't think the value comes into play with the risk.

Managing STRs involves more effort due to high turnover.

The rehab on your primary will help with the cash out refi, there will be a new appraisal which should reflect the higher market value. 

And I’m fairly driven right now to provide affordable housing for my market, but still have needed to increase by 50% at times.

You make money when you buy1) "There is never a bad time to buy"2) "Interest rates are so high right now it kills every deal"

Some places are cheap and look great on paper, but reality is very different as they have higher turnovers and more problematic tenants...they also don't increase in value as much.

Initially I had thought that this company only does property management, but as it turns out they help the investor from A to Z, when it comes to finding appropriate agents, lenders, contractors, handymen, managing rehabs, management, providing advice on the best investment strategy, etc. 

I have seemingly found a good realtor but the mortgage broker has left me high and dry.    

Many local banks and credit unions will do a second up to 89.99% loan to value.

Going this route over high closing costs would save you more money as long as the work can be done in reasonable amount of time.