I tend to agree with Bose-X, because in general entering the US under the VWP program in a private aircraft is not possible.
The reason is that it's the immigration officer who has to determine whether you are eligable to enter the US under the VWP, and if he finds you are not, you are going home on the next flight. Airlines have to sign contracts with the US government to take back any passengers who are found not eligable.
Since somebody in a private aircraft hasn't signed these contracts, they cannot be flown back if necessary, so the VWP is not available to private pilots. You'd have to get a proper visa, which means that your eligability to enter the US is checked in advance (when the visa is issued).
However:
Once you are admitted under the VWP (in your step 2), then this admittance is valid for 90 days or so. If you make a quick visit to another country (Canada and Mexico being the most likely candidates) and then return within this period, you don't have to apply for the VWP again. Your initial admittance is still valid. I have done a weekend road trip to Canada (from Detroit to Toronto and back) by car and all the Canadian and US immigrations officials did was stamp my passport next to the VWP stamp, and drew an arrow pointing to the date that was part of the VWP stamp. No green form or anything else required when re-entering the US.
So I would not be surprised if somewhere deep in the regulations an exception to the VWP requirements could be found that allow you to undertake this trip. Obviously as long as the whole trip falls within the initial VWP period.
But yes, if you simply ask 'Can I enter the US in a private aircraft on the Visa Waiver Scheme?' then the answer will be 'No'.