I know there are other threads concerning this route, but I would like to make certain of one thing.

I am traveling from Tokyo to Hokkaido (not sure where exactly yet) and then back again after 10 days. One of the flexible 3-4 day passes that JR East and JR Hokkaido offer would be perfect for this, however neither will let me travel Tokyo-Hokkaido and there are problems with trying to use both.

It seems JR does not offer a flexible country-wide pass. Is this correct?

If I cannot get a flexible pass then it is cheaper to fly than get a 14 day JR pass. I would rather take the train though.

Yes, this is correct.

If I cannot get a flexible pass then it is cheaper to fly than get a 14 day JR pass. I would rather take the train though.

Flying can be even cheaper than a 7-day pass. It depends on what discount ticket you are able to get.

The cheapest is usually Skymark Airlines with discount fares that can go below 8000 yen one way:
http://www.skymark.co.jp/en/

Another good option are air passes for foreign visitors. Air passes and discounts in general are introduced on the following page:
http://www.japan-guide.com/e/e2364.html