Clutch replacement on that '65

I have never replaced a clutch or removed a transmission from this era car ('65 Barracuda, 360 with 4 speed, And Doug headers. Does the trans typically have to be removed from the car to change the clutch, or can it be slid back enough, without dropping if exhaust is lowered and drive shaft removed?
The bell housing looks trapped above the Doug headers on one side. I don't know if it will pivot much to drop out. The header-to-exhaust flange is just past the bell housing, so I can remove the back section of pipe for the trans, but the bell housing may be trapped.
Thank you again, rjg