I'll try to answer your questions guys....
As far as I know, Splash is the only ride that does this. Of course, we have never tried it on any other attraction...we stumbled upon it by chance the first time, and have always tried to be "riders of the day" since then!
So I suppose it's possible they might do it elsewhere.
Cathy--it's tough, admittedly, to be the first to Splash Mountain. It's whoever rides first...and a lot of times there will be preteens RACING all the way there. So we've tried on multiple times without being successful. It's easiest on an EMH morning! If you can get there then, go to the shortest turnstile line you can find and just use your gut instinct from there. Oh, use the shortcut in Adventureland too!