Hey Michael,
First I think the idea of "do nothing in the first 9 minutes" will unfortunately not be useful as the computed work is mainly there to prevent miners from altering the history of previous blocks. Thus following your suggesting would probably drastically decease the security of the network as less work protects previously mined blocks allowing for lower cost to compute a reorg.
Let us assume the aforementioned point could somehow be resolved there would be another practical issue. It is hard / impossible to sync clocks in a distributed network which I think would be necessary for a system that you propose. (actually Bitcoin is one way of introducing a temporal ordering of events in a distributed network)
Finally even if that was also resolved: How would you prevent miners to already compute the simpler difficulty problem directly after the block was found and publish their solution directly after minute 9? We would always have many people with a finished / competing solution.
So while I appreciate the idea I have the feeling it would be impractical but maybe I missed something.
Best Rene