No real solution but you're not the first to have a problem with this combo.
http://www.uglyhedgehog.com/t-302580-1.html
http://www.fredmiranda.com/forum/topic/1336777/0
Also came across this
Hi, I believe there is a potential issue with using the Kenko 1.4X PRO 300 Teleconverter DGX with the Canon 7D II as well as the 5DIII, 6D, 70D, and IDX with the current 100-400L as well a number of other older Canon lenses. The issue is that the camera hangs if per lens Micro Adjustment is turned on. The fix involves removing the camera battery and lens with the teleconverter and restarting the camera with out the converter. To avoid the problem you can turn off per lens Microadjustment before mounting the lens with the kenko to the camera. If you need microadjustment for the 100-400 with Kenko you can dial in the value by using the microadjustment "for all" setting. It just means that you have to member reset the microadjustment setting when using the 100-400L with kenko. The issue would not affect your T1i but might be an issue with the 7DII. Kenko gave me a refund for a converter when I ran into the issue on my 70D about a year ago. At that time they told me they did not have a converter that would avoid the issue. I don't know if they have made a change in the last year to address the problem.
No idea of it works or not though.