Oh.. well, I've done it all backwards then!
For one handle I did the babywipes before each go at the eraser, and for the other I did a quick wipe, then lots of eraser, and then more of each. They both pretty much turned out the same. Once I'd nuked all my erasers (you get two big ones in those packs you posted about - I cut them into smaller pieces for use) I just did lots and lots of baby wipes, which seemed to remove lots of brown grime as well. Perhaps the eraser sort of removed the thicker top layer and the baby wipes could then do a lot more?
Anyway both handles are still pretty damp, I'll wait until almost dry (but not completely dry as mine is quite old and the vachetta was a bit overdry to start with), then cover them in luverly leather goop. Then once that's all sunk in, I'll give them a good polish, then once properly dry a touch more goop, and a shine.