Were I involved in the decision-making, and assuming the Dementors are not just indestructible but also unimprisonable, unteleportable-to-the-surface-of-Jupiter, and so forth
They seem to be un-imprisonable, as far as I see. They can drain magic and decay matter. So that covers.... everything. Eventually, they'd get out of any ward or prison you'd devise for them.
Remember that Harry's hypothesis of Dementors having no structure but what the wizards involved think of them is untested at best. So they might take revenge if they were suddenly faced with wizards trying to get rid of them.
Even if they do not have any such structure, wizards who started teleporting Dementors to Jupiter would probably think that the Dementors would take revenge on them, and so they would. They're, after all, capable of breeding and barring Dementor-detecting magic(which I suppose is possible) it's fairly unlikely that you'll get all of them.
And yes, it's a bad solution, unless you think that threatening scientists with killing random people unless they invent a cure for cancer is a good idea.
They can drain magic and decay matter. So that covers.... everything. Eventually, they'd get out of any ward or prison you'd devise for them.
You are thinking only of passive static defense, which is an incorrect model that will predict much weaker ability than actual.
Update: Discussion has moved on to a new thread.
After 61 chapters of Harry Potter and the Methods of Rationality and 5 discussion threads with over 500 comments each, HPMOR discussion has graduated from the main page and moved into the Less Wrong discussion section (which seems like a more appropriate location). You can post all of your insights, speculation, and, well, discussion about Eliezer Yudkowsky's Harry Potter fanfic here.
Previous threads are available under the harry_potter tag on the main page (or: one, two, three, four, five); this and future threads will be found under the discussion section tag (since there is a separate tag system for the discussion section). See also the author page for (almost) all things HPMOR, and AdeleneDawner's Author's Notes archive for one thing that the author page is missing.
As a reminder, it's useful to indicate at the start of your comment which chapter you are commenting on. Time passes but your comment stays the same.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: