I believe the value should be based on what the buyer and seller agree to (except for cases where the seller is gifting some value to the buyer or other such relationship based offers).Has anyone heard of such an increase to accessed value for property tax purposes for offers that are not purchased on the MLS? 

That will depend on how long you've owned it and how the "gift" was structured.That being said, the 1031 exchange requires that the tax. payer for the old property and the tax payer for the new property be the same. 

Gifted funds are ok, so no loan needs to be in place.

Would it be a nice gesture to give them a small gift upon introducing ourselves?

This glowing attribute was needed to deliver the gifts and accomplish the mission.Question is, does there really need to be a program that allows ALL reindeers to pull Santa's sleigh, regardless of nose color?

I'd probably give them a gift card or certificate for their patience, cooperation and understanding.  

Thanks Ofgift Gift for your quick reply!

First time buyers often buy homes with a gift as their down payment, so they are really short on funds.

Well I have to confess, when I was a beginner Investor years ago I used to just send my contractors each a  gift card for $50-$100, and my thinking was that I did show them that I care about them.

Gift is supposed to be one of the inseparable part of this big celebration.