I have an iPad Air that I bought specifically for the Inspre, and I hope that the iOS app comes back... But I'm not holding my breath. This is completely up to the whim of Apple Inc. at the moment, and they have been known to refuse apps for all kinds of reasons.
That said, if I was going to get an Android tablet, I would go for one that works well for games. That way you can be sure it will have a) Lots of RAM, b) good horsepower, and most importantly, c) a good Video processor.
The NVidia Shield looks good in that regard. It's only downside is short battery life, but even if it's 3 hours, it should still outlast the Inspire/remote.
I'd stay away from the "cheap-o" androids, unless you want choppy video.