Is it legal to compensate a CFI for more than 8 hours of his services per day?
In my scenario, a CFI is required to be aboard a plane to satisfy
  insurance requirements.


This is the important line and you need to reference the policy for the exact wording. I happen to have some quotes from when I was shopping for an M20C about a year ago and here is the exact wording from my aircraft owner policy, 


  Named Pilots and Additional Pilot Requirements
  
  You are to receive a minimum of 5 hours dual flight instruction in the
  make/model by a CFI who meets all the requirements of the policy and
  receive a written endorsement in your logbook from the CFI prior to
  solo; then 5 hours solo in the make/model prior to carrying
  passengers.


In this case it clearly states that the time is all flight instruction and not simply "CFI present" time if your policy is written this way then its pretty clear the FAR would be broken in your scenario. I think its safe to assume most policies are written this way although if the policy simply states CFI on board then its tough, although I agree with Ron's comment its going to be hard to explain as a CFI that you just "sat there".