Some of my first branch tops cracked too. The wood was still too wet.
I needed a fast way to dry the wood so that it wouldn't crack. The microwave oven worked very well. It heats up the wood all the way through and drives the water from the inside at the same time as the outside. Some woods work better than others. One minute is the longest you ever want to cook without checking for dryness. If my glasses fog up when held above the wood, it is still too wet. The wood will start on fire from the inside if you microwave too long. Just trust me on this one. You don't want to find out for yourself.
Jamb chucking is a way to turn without a jaw chuck. It does not work so well with softer woods though.
Screw chuck is another option. Drill and tap the wood, then screw it onto a threaded rod driven by the headstock.
You will find yourself making all kinds of special tools for you lathe. If there is a will, there is a way.