I was told that as long as the land is in contract to be purchased, the construction loan could be approved by showing renderings to local banks.

NOI is multiplied by a cap rate that fluctuates under market conditions.This formula renders how the asset is 'actually doing' in the current market.

I'd say you handled the situation well by explaining what you do, how it works, and why you deserve to make a profit for the service that you render.

Appraisers are on the side of protecting the bank but are supposed to render honest and fair opinions.

There is software that the professionals use for pricing big jobs, I like chief architect for material take-offs and renderings.  

From my experience clients are very rewarding experiences, as you get a chance to bring someone else's dreams come to life, personally I love to take them through the process of a full renovation, everything from rendering to build, however, if you are not built with the proper infrastructure it is incredibly time consuming and administratively intensive.

@Steven PaulCan't render an opinion on tax deeds or liens, Steven.

The window would go into the back porch which would render the room a closet again.

I'm just not sure if the owner will be willing to sell and render my rent 1075/month for a mortgage payment of approx 650/month. 

I like the idea of getting a rendering to give your potential clients a base idea of what they may be getting.