Can I cheat AT&T and Sprint when switching between them? Details below?

At this time my family of four all have iPhone 5's through AT&T. I saw that Sprint has a better family plan than AT&T (and that they would buy me out of my current contract). So I'd like to switch; but I was wondering if I could in a way cheat AT&T and Sprint by upgrading all our iPhone 5's to 6's through AT&T's special "upgrade to the new iPhone ever 12 month and pay tax up front then the rest over the next 12 months" thing. So basically will the following circumstance work. { I have all of my family's iPhone's upgraded to iPhone 6's through AT&T (only paying the tax of the phone) then right after that I go to Sprint and they buy me out of my contract with AT&T. The Problem is that there's a couple thing that I'm not clear no they are.
-can I actually switch the iPhone from AT&T to sprint
-what will sprint buy me out of?
I saw that they will pay as much as $350 on every line. So does that mean they will pay off the contracted price $199 and $299 for the 6 and $299 for the 6 plus or the full price from apple $649 and $749 for the 6 and $749 for the 6 plus?
I could really use some help organizing and understanding all of this information. Thank you so very much for any help that you give!

Plan sounds perfect, go for it.

Buying you out of the contract means paying the contract termination fee.
It doesn't mean paying any previous amount you owe or paying something that is not related to the contract termination fee.

You can't be that stupid, can you?
But then again you may be? What does not sprint offer - low prices and poor reception.

They'll pay any termination fee. You'll pay anything else you owe, including the remaaining amount for the new phones.

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