Regardless of who the procuring cause is (the broker), the same amount of paper work, and time is involved. Your problem is that a broker has already shown you the property and they have become the procuring cause.
Any reputable agent will not touch a home that has been shown by another agent.
By the way, you don't get anyone the 3%. The seller is paying the commission.
You're plan has back fired. Sorry.
Regarding the seller's agent being entitled to 6%, my question is - seller's agents painfully explain that they represent seller's interest etc and make you sign the relevant forms .. Still they are entitled to 6%? I am not arguing, just trying to understand the dynamics.