I have an issue that's related to this topic that you could probably shed some light on.

This is an old article I wrote, but may shed some light-https://www.biggerpockets.com/renewsblog/2013/01/2...Hope that helps!

Search that and you will find lots of discussion that will shed light on this issue.

Hopefully it will shed some light on my situation!

Hope that sheds some light on your query.  

I guess I could buy a storage shed from Home Depot and throw it up somewhere and call it a "tiny house!"

Cash has weight but not as much as investors think.If my seller wanted a cash buyer in that instance we would simply reduce the price down until we found one who would pay a premium.Example from 3 mill to 2.9,then 2.8 etc. and get cash at 2.7 to 2.6 instead of 1.8.ORThe seller could do a wrap with 20% down and sell for a much higher price.If you applied the 50% theory in some areas the property would be gone in a few hours at those levels.50% is like hitting a grand slam when most hit doubles.Depending on the area the 50% theory does not always apply.It is simply a guideline where other factors have to be taken in.

Does a verbal offer carry the same weight that a written offer does?

I would give greatest weight to the length of the hold.

Not sure I shed any light on your decision but that's my two cents.