Bill - One of my fave guitars over the years is the Ernie Ball/Musicman Eddie Van Halen guitar from the early 90's. It has an oil finished maple neck and fingerboard with a thinner finish then most Musicman instruments and really attracts shows the grime.
I called Musicman about the best way to clean the board and Dudley Gimpel, their main designer actually got on the phone.
Their best recommendation was to use Murphy's Oil Soap (available at your local Target), diluted with about 4 parts water. If that doesn't clean the board sufficiently, then you can go with a stronger mix. Rub gently with the grain. I found it worked really well and was a better solution than the automotive 3M scrubbing pads that I was thinking about.
This leaves you with a clean board down to the oiled finish.
I have sometimes rubbed in a coat of wax, but it doesn't seem to last long on the fingerboard or delay it from getting dirty again. I am fond of Livos Gleivo liquid wax, which is a German beeswax/carnauba blend that's supposed to be all natural (but smells like it's all solvent). I got this many years ago at MacBeath Lumber in your neck of the woods, at their recommendation.
Give the Murphy's Oil Soap a try!
David Fung