Greg - that is an awesome washer...it was my very first machine, the one that I grew up with! Mom bought it in early '63 and it's still going in my old aunt's basement in NY. Still washes well, she says. Unfortunately, it is rusting badly and it's matching gas dryer died years ago, but what a neat set. She only uses it a couple of times a week, if that much. She's selling the house now, so guess it will be gone for good soon.
I do not remember that washer leaking tranny fluid when it was tipped forward or moved in any way. When my machine was just a year old, it did exactly what you are describing, and Easy service had to replace the transmission. After that it was good as new. Don't remember if it was leaking at the time though, but the transmission had gone bad. Hopefully this isn't the same problem you're having, but sounds very similar.
I'm not sure if this is correct or not, but maybe Robert can confirm, but I think there is a relay switch inside the timer that turns the machine on and off. If yours won't turn off, the relay switch might be bad. If I remember correctly (and really not sure about this), that thing was red in color. Maybe just dreaming....it was a long time ago.