What if the institution just doesn't have an appetite to finance that type of asset anymore?  

It depends on your appetite and financially where you are in your RE career. 

the rate always depends on investor's appetite.

Some of the big guys like Wells Fargo or Bank of America might not have an appetite for a small loan.  

That means lot's of locations and restaurants.Here are some resources that might help you out some.Book to read:  https://www.amazon.com/Appetite-Acquisition-Robin-...Website with podcast about restaurant industry.  

I'd even consider a cash out refi on a rental just to pay off the primary (that's just my appetite for debt).  

   Hey guys I'm new to the forum, I just stumbled upon the forum yesterday, I'm 23 years old right now I've been flipping used cars and doing contractor work for the past year and i've saved enough of my profit to purchase my first property, any advice, tips, book recommendations, courses or thread recommendations would be greatly appreciated, I'm in a mode where I have an immense appetite to learn and absorb content.Thanks,           Quin

There's so many ways to make it work, that I hesitate to advise on the "right" option - it all depends on your risk tolerance, appetite for leverage and long-term goals. 

You're best option to get all these questions answered is to find a local/regional bank (local to where you want to build) and see what their appetite and offered terms these days for construction loans. 

I would think that short term prices would suppress on SFH's but from a little bit of online research about the RE effects of other hurricanes, that seems not to always be the case as demand goes up as rescue money and recovery related personnel pour into the region.