With Neil's help, we think we have it.
The below is a reg file that will increase the jumplist to a higher count, you can change it if you like:
Unzip it, run it, accept all the warnings and it should look like this (Notepad example):
If you need to change it more, it is better to edit the reg file and rerun it unless you are comfortable with editing your own registry.
What you want to edit is:
Changing the 15 to something else (doing so in Notepad is fine).
Hope this helps.
Stardock Customer Service Manager