Interesting thoughts sir. Due to the shear size, gravitational force and energy emission of such objects I find the 'cage' idea highly unlikely, close to impossible even.
Although, if we can manage to make a cage of such a rediculous size and have some form of super power anti-gravity field in our technology arsenal, then maybe ;)
I would say your idea of feeding off the energy produced by Hawking Radiation is likely the only possible solution to getting energy safely extracted and useable from a black hole and the most likely choice.
Personally, I highly doubt humans will get anywhere close to such a time in our universes existence. However, if they do manage to live that long then I think they are more likely to feed off the energy of neutron stars and once they all die out that will likely be the last of their days.
That of course is just my opinion :)
Thank you for sharing. And yes, highly doubtful we will make it that far.