Hi Allan, you very probably don't want to hear from me as I have not achieved a high level of proficiency with F#, but I have set myself the goal of getting there (much like your self).
I thought I might suggest what has turned out to be my biggest learning tool: Stubbornness.
I set my self a large-ish project (a game, just as gradbot suggests). I then decided to code using as much immutable data as possible regardless of the performance costs.
Then if I couldn't find a way to use immutable data I'd come here and ask for help.
The hoops this stubborn approach forced me to jump through has been a brilliant learning exercise, as (just as Juliet mentions) F# allows you to write really ugly C# if you let your self get lax.
Right now I have tile based 2D world and a little man who can find his way to the treasure and back home again using A* path-finding ... The only thing I mutate is the title of the window it's displayed in.
I only got serious about learning F# towards the end of July (I'd dabbled before then) and this project has taught me a huge amount, along with the help of the guys here at StackOverflow.