Sometimes you don't care who approves the project you send in a ringi process; you just want it approved as soon as possible.
This is often the reality in everyday business and a real demand in workflow systems. An easy way to solve this is to give more people the right to approve things.
In the above workflow all people with approval rights can execute the "Quick approval" task. If your organization is one with about 100 employees, just give this to all board members. Board members will not hesitate to give out those approvals if they know it's within their authority. And, if they have smartphones they can do it 24/7!
(Watch someone give an approval with an iPhone app here.)
One more thing—if board members want to share their approvals with each other, just send an automatic email to the board's electronic mailing list.