360 Married to A833?

Depending on how wild you're going with the 360, you really don't NEED to swap in a bigger flywheel and bellhousing.
You can upgrade the clutch to a 10" scalloped pressure plate, some slant 6 applications used this combination.
A competent clutch rebuilder can also up the clamping pressure by adding extra springs with higher pressure rates.

I believe there is actually a diaphragm style pressure plate available, which helps lighten the pedal pressure, yet clamps good.
It would still need extra spring pressure added for anything you want to sidestep the clutch on.

As far as the flywheel goes, acquire a balanced B&M flex plate for a 360, take it and your stick flywheel to a crankshaft balance shop and have them match balance the flywheel to the flex plate.
Done this several times and it works great.

Mark.