Those of you who read the previous entry could notice in the comments that it did not take long for Don Syme, the designer of F#, to offer to help resolve the issue.
Less than a week later I had a new version of the FSharp core library tailored for the Xbox 360 in my mailbox. To the F# OSS team (Don Syme, Laurent Le Brun and Tomas Petricek): big thanks to all of you!
What took a bit more time was to build a Visual Studio 2010 template for projects using the new F# core library. Thanks a lot to Dan Mohl for his help. He is the author of templates for F# + Silverlight + WP7 projects, which are available on the Visual Studio gallery.
It's the first time I make a Visual Studio extension package, I hope I got it right. It's available on the Visual Studio gallery. If you try it out, please let me know if it worked for you (or if it did not).
A small but important note: In the project properties, the build tab has "generate tail calls" unchecked, both in Release and Debug builds. That's the way it is meant to be. If checked, your game will crash with an InvalidProgramException.