A brand new spool is a good idea. It is the most critical piece of the top.
As I see it, there are 3 main factors that you can work on that will determine your maximum rotation rate:
1. Weight on the cart = total energy available
2. Mechanical losses due to friction along the rope path, possible pulleys misalignment, etc.
3. Minimum diameter of the spool core = final gear ratio
In principle you want the smallest spool core diameter possible. Perhaps you need a longer belt pigtail at the end of the rope.
The maximum diameter of spool is not critical, but will be a factor in how smooth is the acceleration, what is important as any jolt will decrease the efficiency.
Happy new year to you: 2015 is the year of the big record!