Since the car and motor matches, may be wise to rebuild the motor and trans for insurance. Very hard to find a numbers matching 67-9 Firebird and the difference in value between numbers matching and non is approximately $4-5000, higher for convertables.
Before you start to really enjoy the car, I would consider thoroughly scrutinizing the operative concerns before possibly causing irreperable damage.
I do not want to be a kill joy, but if you just can't nail the problem, tear it down.
Si Vis Pacem Parabellum
1967 Starlight black PMD Engineering 400 Auto 1968 Alpine Blue 400 4 speed 1968 Verdoro Green 400 HO 4 speed 2013 1LE 2SS/RS Inferno Orange Camaro.