Is this "easy" to do? I was there alone last year and was privileged enough to be able to ride the Lily Belle
I'm hoping riding the engine is a little more "commonly available" than the Lily Belle ride, as I'd love to do this when I go back in just under 2 weeks - is this the case?
It was pretty easy the time we did it. You just have to wait until the right train comes around. I can't remember the engine name but I believe there is only 1 train that can take riders on the engine. I would think it would be easier than getting a ride on Lily Belle. I haven't tried to do this yet.
As long as no one is waiting already, and the train that takes riders is being used that day, you can ride along. If someone is already waiting, you can always come back.
When we did it, it was in May (must have been 2008). It was a pretty hot day. We asked one of the CMs there if we could ride and she said "yes" we would just have to wait for the train to come around. It had just left the station. About 15 minutes. Told us to wait off the side and she would get us when it came.
We did have a problem though, the CM we spoke to apparently took a break before the train came and even though she said she told someone else, the train we were waiting for came, and went, without anyone riding in the engine.

I thought it was the right train but figured they (the CMs) would come to get us. I asked another CM and he said he didn't know we were waiting and that was the train we wanted. We needed to wait 20 more minutes. I wasn't very happy but at this point we had waited long enough that I wanted to wait to ride it. He was very apologetic that he didn't know we were waiting and gave us a "front of the line" pass to use anywhere in the park (except Nemo).
It was interesting riding. But it was pretty hot.

I would do this again but not in the heat of summer. Also, make sure you visit the restroom before you board, you can't get off early. DD was fairly dancing in her seat from TL station to MS. We sprinted for the bathroom when we got off.
Like I said, I would do it again, but I think we liked the Mark Twain a little more. Plus, we didn't have to wait at all. Cool thing was that the CM we spoke to took us around to a side gate and we got to get on before anyone else boarded. Made us feel like VIPs.

We did it at twilight so it was pretty out.