OK, so it’s time to part ways with Ninject. It’s too slow (http://cardinalcore.co.uk/2015/01/28/ioc-battle-in-2015-results-using-ninject-think-again/), and it doesn’t want to change (https://github.com/ninject/Ninject/pull/102).
Ninject was fast enough at first, but as apps get bigger, its performance and CPU cost get too high.
Simple Injector has a near-parity feature set (support for MVC filters isn’t quite as strong), great documentation and excellent performance.
Migrating the setup is also pretty straightforward.
Hope it helps someone else…