Quick look at the other answers: it doesn't seem like you are doing something so different that there is something fundamentally wrong with Ninject that you would need to modify it or replace it. In many cases, you can't "go straight for [the] internals" because they rely upon unresolved dependency injection; hence the usage of Ninject in the first place. Also it sounds like you already do have an internal set of interfaces which is why the question was posed.
Thoughts: one problem with using Ninject directly in your SDK or library is that then your users will have to use Ninject in their code. This probably isn't an issue for you because it is your IoC choice so you were going to use it anyway. What if they want to use another IoC container, then now they effectively have two running duplicating efforts. Worse yet what if they want to use Ninject v2 and you've used v1.5 then that really complicates the situation.
Best case: if you can refactor your classes such that they get everything they need through Dependency Injection then this is the cleanest because the library code doesn't need any IoC container. The app can wire up the dependencies and it just flows. This isn't always possible though, as sometimes the library classes need to create instances which have dependencies that you can't resolve through injection.
Suggestion: The CommonServiceLocator (and the Ninject adapter for it) were specifically designed for this situation (libraries with dependencies). You code against the CommonServiceLocator and then the application specifies which DI/IoC actually backs the interface.
It is a bit of a pain in that now you have to have Ninject and the CommonServiceLocator in your app, but the CommonServiceLocator is quite lightweight. Your SDK/library code only uses the CommonServiceLocator which is fairly clean.