If a State or Federal regulator cannot find an exact way to pin this marketplace down, then they go after intent.
Barring the problem the marketplace will face with respect to trust, etc. let us look at the intent.
The intent will clearly how that without the market place, the transaction cannot take place. How will the marketplace make money? If you extract a fees for the exchange, you just made yourself party to the transaction and now depending on the regulation, a state may deem you as a money transmitter, but it would be difficult to do so.
However, from a consumer protection point of view, you could be liable for it. Because you are also playing the role of a matching engine, the securities and exchange commission might deem you to be an unlicensed exchange and ask you to obtain a license.
As long as the two parties are conducting the financial transaction themselves directly, and the flow of funds is through their respective financial institutions, you ought to be okay and not classified as a money transmitter.
This idea however, is not new. Building trust on a platform that is self-governing, is not easy. Bad actors will find a way to play the system.
All of course is an IANAL (I Am Not A Lawyer) opinion.