I was struck by the degree of naiveté you exhibited by suggesting the possibility of a unitary group combining those whose interests are opposed to GA (restricting the meaning of GA to individual ownership of the aircraft). The airlines despise GA.
The airlines are run by financiers, not by the pilots. And I am suspicious that airline pilots see GA as a safety hazard and would be unlikely to oppose their employers. The NBAA also despises us for similar reasons. AOPA is only interested in promulgating itself for job security, very similarly to the AARP. The EAA has changed so much that I am not currently able to ascertain its leanings. The FAA is opposed to any GA issues. They will not tolerate a GA aircraft in Class B airspace if there is any manner available to them, due, I suspect, to the inconvenience of the disruption caused by dissimilar airspeeds. They use their power to constantly expand all Class B airspaces. I suggest your proposal of a supra lobby is most likely met with polite yawns by all except the naive.
I forecast that GA can expect to receive more “ramming it to us” in the future, with the support of the airlines, the NBAA and the Department of Homeland Security.