The inbound (Mono -> Gecko) C++ DOM function is working fine and I can recieve a C# call in JavaScript; now I just need to pass it off to the actual function.
There was a bit of trouble initially as I couldn't obtain an nsIWebBrowser pointer from gtk_moz_embed_get_nsIWebBrowser. This turned out to be because the Gecko# WebControl hadn't been shown yet (i.e. window.ShowAll()), but I didn't figure this out as other functions like gtk_moz_embed_get_location worked fine.
Implementing the ASP.NET GUI designer with Mozilla's Gecko web rendering engine is an obvious decision: it's open-source, has strong standards support and a large feature set, is highly extensible and flexible thanks to its XPCOM component system, and using Gecko# it can be embedded in a GTK# GUI. Mozilla is becoming an application platform, with XUL for declaratively writting GUIs, and JavaScript for program logic.
Gecko# wraps GtkMozEmbed, which is a C GTK widget, hiding Mozilla's native C++. Understandably this widget isn't bloated by wrapping the Mozilla DOM or other internals: it claims to exposes enough functionality for "about 80% of uses". Essentially this means a basic web browser.