If you view their search results enough you will see that low price trumps almost everything else; there's no other logical reason why a host with a 4.1 rating with say 40 reviews would come up higher in a search than one with a 5.0 with 25 reviews, all else but price being equal. 

Request a price reduction equal to the discrepancy between the assessed and market values.

Higher price points are all things equal better for building equity, lower are better for cash flow flow. 

To do this, they have to pay a termination fee equal to 1.5x monthly rent, give 30 days notice, and let me market the property during their last 30 days of occupancy.

In the grand scheme of things, it doesn’t really matter since we’ll be getting married anyways, but just for peace of mind, or if something goes wrong, do you think it would be smarter to go with a HML so we are equally taking the risk financially?

Your heir will inherit the property and receive a step-up in basis equal to the market value at the date of your death.

We were exploring taking out a primary mortgage on their home to take out 350k in cash at about a 6% interest rate, and I take out a loan from them at an equal rate or slightly higher (maybe 6.5%).

Again the US Economy is remaining quite resilient.All things being equal, this would be good.

In scenario B, my offer is equal.

Ok, appraisers aren't perfect or created equal.