the flight envelope as I understand it is not quite as nosefirsteverytime described it - it is rather G-forces on the vertical axis (plus and minus) plotted against airspeed on the horizontal axis.
Actually, there is no single "envelope" when it comes to aircraft performance. The total performance "envelope" is represented by a series of graphs, charts, and tables that represented the designed, tested, certified, and/or operational limits of performance.
Common charts/diagrams include altitude vs airspeed, weight & balance, gross weight vs G forces, airspeed vs G forces, and a host of others.
We are in agreement that "Pushing the envelope" does seem to mean taking the aircraft to the extreme of what is permissible.
That part is true. Often the pushing is beyond what is permissible to the limit of what the aircraft will endure or what can be attained.