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Coming from the EU, I am in the process of getting a DV visa, and planning to go to the US for reconnaissance mid-June.
When entering the US, I understand, the border patrol has the right (even with a valid greencard-eligible visa) to turn it down, and cancel it for arbitrary reasons.
In contingencies like this, would applying for the Visa Waiver Program as a next-best-alternative let me enter the United States (for the VWP period)?
If you have any kind of valid U.S. Visa in your passport, you should not do ESTA. It wouldn't matter because whenever you have a valid visa, the VWP does not apply.
If you are still waiting on your visa to be issued you can enter on VWP and tell border security that you are on a personal exploratory visit before your green card is issued, which is perfectly acceptable. Don't ever lie about your true intentions. If they determine you haven't been telling the truth it could jeopardize your visa application.
Note that you can't apply for VWP. VWP means that you don't need a visa for simple tourist or business trips. You do apply for ESTA if you arrive by air or sea (so if you enter via Canada you don't need ESTA).
If I understand the question correctly, you seem to be thinking that if the immigration officer says 'entry denied' (which is unlikely if you have a green card), you would then say 'OK, I'd like to enter under the visa waiver program'?
This will not work. Apart from, as stated above, the inapplicability of the VWP if you have a valid visa, you don't get two chances. The officer would have a reason for not letting you enter, and you would be bundled off to a waiting area for the next plane back home.
