Broken & bent rods on logsplitter cylinders are pretty common. There are many causes, but design of the pusher, and mounting of the cylinder are the usual culprits. The cylinder should be mounted at only 2 points, one on the pusher, and one on the cylinder (usually at the base end with a clevis or cross pin). Avoid the temptation to put a u-bolt or other fastening near the rod-end of the cylinder. When the pusher goes out of line with the cylinder axis, it bends the rod. If you're lucky, it only puts side stress on the cylinder gland and wear on the side of the rod. Unlucky, and the rod buckles. It will always wiggle a little though, so you want a flexible attachment between the rod & the pusher.
The pusher should be WELL guided, so that the cylinder remains in line with the beam regardless of what a knotty chunk might want to do. Longer side guides help. Usually if the flat plate is on the rod end, and the wedge at the end of the beam, there is less side force on the pusher. But this isn't always practical, I know.
As for cylinders, there are cheap cylinders, and there are good cylinders, and they're rarely the same. The new Prince tie-rod cylinders have heat treated rods with nickel-under-chrome plating. They are far stronger than the cheap cylinders being imported from every third world country you can name. Check our web site if you want a good one - CylinderServices.net
As for cycle time, the guys are right about larger pumps & smaller cylinders making faster splitters. I personally think a 4" bore cylinder is all most people need for most splitting. With a 16 GPM 2-stage pump it will make a nice splitter. Larger cylinders put out more force, but you pay for it with slower cycle speed. If you really want 16 GPM though, you'll probably have to go to 3/4" hoses & fittings, and a valve with 3/4" ports. 1/2" lines will work, but if you checked it with a flow meter, you'd probably find you were getting less than 16 GPM. We've got some good deals on 2 stage pumps too.
Good luck getting it back together.
Don the hydraulics guy