Use a big piece of pipe (long, not heavy), or a 1.5" piece of round bar stock...1'-2' long.
Slam that thing in there like a giant slide-hammer and bang the handle out.
I haven't tried it with a counterbalanced handle, but I have done it with a non-counterbalanced Cataract handle. It works.
The counterbalance is a big steel rod, about 1.125" diameter that is epoxied into the handle. I think Cataract's standard counterbalance is about 4lbs. Half as much would feel better to me.
@Electric-Mayhem, I think hammering it out with a pipe worked better than the heat gun. We tried it both hot and cold, and it was the hammering that did it.
I'm sad you're not replacing the woodies with more wood!