This weakens the idea of having individual houses in LLC's, at least in my mind.

The seller keeps the earnest money and there is potential for legal action.There are some weasel clauses that might make you feel a little better about not being able to find a buyer but they significantly weaken your offer.Good deals sell themselves so getting one is your first priority.

Basically what my realtor was told by the seller's agent was that they're firm on the price that was offered(my offer was implied to be the strongest) and if I put a contingency, we think that it may weaken the offer if they are worried about a low appraisal. 

Even while national housing trends weaken, growing markets like Chattanooga and Nashville will likely be insulated from the harshest adjustments coming.

Homes are spending more time on the market and the pace of both home sales and price growth is slowing...This normalization does not necessarily mean a weakening housing market, but a return to less aggressive market conditions."

The fact that you converted to a rental property can even weaken your position even more.

Right now, the mortgage market is weakening and lenders are either pulling out or tightening credit.

Laws also change that can weaken the structure such as anonymity in Swiss accounts has been severely curtailed in the new anti terrorism laws. 

You could weaken the tree and it may fall in a heavy wind.  

It's great for me because it gives me crucial insight into their wants / needs and their initial position of power just continues to weaken the more they talk.Ok, so again...open to suggestion & ideas.