Simple answer, $$$$$.
Most of this has already been said but to gain speed, you need large pump, large motor to spin it, large hoses to handle the flow, and small cylinder with a large rod.
If the cylinder isn't broken, it isn't worth replacing as it is the most expensive part.
To turn a larger pump, you will need a bigger motor. If you can find an old riding mower with a good engine for free, you could step up to a 22 gpm pump for about $200, but you will be on your on for mounting the motor and pump. Then you will need 3/4 in lines. (Does the cylinder and valve have 3/4 ports?) You may need a bigger hydraulic tank or oil cooler to deal with the heat generated by the higher flow.
So bare minimum, if you score a free engine (12 hp minimum) and get the engine mounted using your own fabrication skills, so all you have to build is a 22 gpm pump and pump mount, you are looking at $300. Also if it came with 3/4 hydraulic hoses (doubt it) so you could simply hook up the lines and start running, you can have a 7.3 second cycle instead of the 11.5 it came with.
$300 for 4.2 seconds is based on very best case scenario. More realistically you should throw in an extra $150 to upgrade your hoses. If you have to buy an engine, add in another $300-$600. Some vendors sell engine and pump log splitter build kits that start at $400 but to get a faster rate you may be looking at $800+ for just the pump and motor. In the end you could spend $1200 to get a 4.2 second faster cycle time.
The real question here is how much are you willing to spend to gain a few seconds per split?