I use KlausT and had similar issues.

First, I had crashing issues as well when I combined different types (1070 with 1060's in my case ) in the same mining program.

Run them in separate instances and then see if one of them crashes. if it does, then you know which cards aren't liking the oc'ing you're doing. If not, then they simply didn't like being together, at least that's what I've come up with.

This tech has worked for me until I can fix the problem completely.

also, to add what I've found stable for my system, I have two rigs. I run 4 1060s in the same instance and no issues. On the 2nd rig i have 2 1060's running together and a single 1070 running in a solo instance. I found that the 1070 didn't like my aggressive oc'ing, so I backed it down a bit and so far 6 hours and no crashes.

Edit:
I just noticed you said the WHOLE rig locks up? damn, maybe a short or power issue?