Differences between "just might" and "might just?"

Can someone help me understand more precisely the connotative differences between "just might" and "might just

I came upon this dilemma while working on a short comic strip. In the first panel, a person is attempting an unorthodox approach to a problem, saying:

It might just work.

The second panel, moments later:

It didn't work.

I'm unsure if the effect would be significantly altered if the words were swapped.

Solution 1:

"might just work" sounds like "it might simply work--that is, without the complications one might predict."

"just might work" has a blossoming optimism. It suggests that something that you'd think wouldn't work actually has a decent shot at working.

Solution 2:

"It might just work" more sounds like positive and pragmatic Eg: You are working on a research and you finally say " It might just work" seems like you are hopeful & have some sort of surety

"It just might work" sound more as a natural occurrence & skeptic. Eg: You are stuck with your car left not working you say "it might just work" a little less hopeful plus relying on luck to work it out for you.

Solution 3:

I think It might just work could also suggest the meaning "It might work, but barely". With the annotation that the purpose will probably be fulfilled, but only that and nothing more.