I could run my 385 in my sleep so we can assume I'm very comfortable with it and know it's limitations.
When I'm on slopes it's not so much the tipping its the sliding you have to watch. Soil conditions will be key. Nice smooth motions and keeping your weight in close to the machine and you won't have to worry about the tipping much. I've been on a 2:1 with my tracks sideways digging and then dumping full buckets down hill. Stay close to the ground and get your bucket in tight to the machine before you start swinging and you just slide the bucket down the slope so you aren't picking up a track (or learning how to dump and catch yourself lightly and lower back down so you aren't abusing your U/C).
Another thing is your bucket weight. Anything past say a 3:1 (just throwing that number out) and you're not gonna be able to swing a full bucket uphill unless its tucked in tight against your machine. I've been on slopes that the only way I could swing uphill was to start to swing one way, then use the momentum/gravity to swing back around the other way.
Sliding is your enemy. If you don't have good footing (wet/power/loose rock) you'll be dragging yourself around trying to dig. And tipping becomes a hazard during the slide. Lets say you're mid swing (can't catch yourself), full bucket and the machine takes off on you. The slide isn't so much the problem its when your track catches again quickly and transfers all that weight. Over you go!
I'll take my 385 anywhere, but everyone thinks I'm insane so take that into account. My advice: if you aren't comfortable don't do it. You have the right to refuse work you feel is unsafe. Your foreman also has to realize that on slopes like that you better be billing hourly cause you wont get much production picking around with half buckets and repositioning all the time.
Here's a video of me on a fairly gentle slope loading out a ramp. Once I started sticking out I had to hold full right swing just to stay in place. That should give you a pretty good idea of how you have to account for all that extra weight when you're trying to work. Also the return swing was slow because I wasn't actually swinging, I was just letting gravity pull it back down and then trying to stop it before it overswung my target.
http://www.youtube.com/watch?v=8yLGqxqzJPM