Since I installed this sign on 28 September, the Whimsy steam train has made 206 trips (many with multiple avatars). The current count stands at 23,651. That's an average of 5.6 trips per day-- about what I estimated.
That would suggest some 13000 trips since Whimsy was born in April, 2008. Since at least half the trips carry more than one avatar, 23,6521 trips seems a reasonable guess. I'm leaving the sign as is.