I think you’re basically on the right track – If you have not already I would suggest taking a look at Rhino Igloo, an WebForms MVC framework, Here’s a good blog post on this and the source is here – Ayende (the Author of Rhino Igloo) tackles the issue of using Windsor with webforms quite well in this project/library.
I would cache the reflection info if you’re going to inject the entire nested set of controls, that could end up being a bit of a performance hog I suspect.
Last of all spring.net approaches this in a more configuration-oriented way, but it might be worth taking a look at their implementation – here’s a good reference blog post on this.