My problem is that I was naive and signed an exclusive agreement with them that has a clause stating that if I buy a house within six months of termination of the contract that they showed to us or we inquired of them about it that they are still entitled to the commission.

Help for Airbnb and Vacation Rental OwnersWhile long-term effects on the short-term rental industry are debatable, here are some things you can do right now:Reduce your vacancy rates as much as possible by offering discounts and being more flexible during this timeCut your expenses by eliminating welcome gifts, reducing amenities and subscriptions or applying for mortgage deferral programs, as discussed aboveIf you’re an Airbnb host, apply for cancellation reimbursement under the $250 million Host Relief Fund available for qualifying cancellations (up to 25% reimbursement of what you would normally receive from a canceled booking)Consider turning your short-term rental property into a long-term rental, at least for now, as the traditional rental market is not expected to be impacted as severely as the short-term rental market  Additional ReadingResources for Property Owners and Agents from the National Association of Realtors is a great list of general recommendations and resourcesList of Relief Programs Offered by US Banks, published by the American Bankers Association, is a comprehensive list of specific measures banks across the US are taking to help borrowers in needCOVID-19 Tax Resources Center by the Drucker Scaccetti tax services firmLegal Guide for Landlords by Julie Anderson, written for the Mid-America Association of Real Estate Investors, provides general legal guidance and advice for real estate investors  Please let me know if I missed anything, or if there is any inaccurate information, so I can correct it.  

Would I be able to claim the exclusion of gain for my primary residence and claim a partial exclusion for my renal or vise versa?

Real Estate industry can be the answer to your dream. 

It's their house, and they can choose to sell it however they would like.The language from the policy is below:Section 1.3 Exempt ListingsIf the seller refuses to permit the listing to be disseminated by the service, the participant may then take the listing (office exclusive) and such listing shall be filed with the service but not disseminated to the participants.

He's not saying it, but something about his 4 hours comment makes me believe she comes with a industrial grade agitator.

Since we're talking about a primary residence , you could also mess up your 121 capital gains exclusion if you sell within 3 years of making it a full rental.More risks than potential rewards IMO.

I work in the insurance industry and as rates have certainly increased this year, most everybody that I have come across have had similar increases in numbers. 

The renters are in healthcare industry and have secure jobs.

They will all sell their services as something unique and quote their years in the industry.