Honestly, our Akita is 2.5 and does this nearly every day~ he has been trained (aced all the tests), used the crate as retreat/punishment/timeout refuge, rewarded with treats and attention, given consistent commands (the same word every time), we have established dominance (obviously, he feels comfortable at home and so this is still a work in progress), etc. This, we have been told is a "game" and not to put too much emphasis on it and it will pass as he matures. He,fortunately is equiped physically to stay outside so that is what we have had to do in a pinch. He has doggie door access to our garage (which is like his bachelor pad - it hasn't housed a car for 2 years) so he always has a place to go.
It is an awfully frustrating problem~ one which I would love to hear your eventual solution to. I will try the lead if you have success..I would be happy to hear!
Best of luck~
Kristen