I don't know what a 6 weighs, but I sling my late model flat V8 and HD 3 spd tranny around on a 2 ton cherry picker. The engine alone weighs 569# Your six should be lighter than that. Only caution is to make sure your lift has 4 feet/rollers (not 3) for weight distribution so it doesn't want to go over sideways.
A 2 ton hoist is more than adequete for pulling the engine. I have pulled my flathead 6 and trans with a 2 ton hoist with no problems. Same hoist has been used for multiple engine swaps in a few of our projects.
Remember to look at where it is rated as two tons. Some units are rated as 2 tones with the arm fully retracted and go down as the arm is extended. If the motor and tranny are half the weight of the truck it would be a ton or less.