I think the issue is that all of the channels have the same common ground. If that's the case, I doubt your scope is going to behave any differently unfortunately.
I tried just using a single probe across the resistor and that also doesn't give accurate readings. Additionally, once you approach ~0.75A it starts to severely distort the signal, so much so you can easily hear it in the sub.
Next I used a cheater plug on the scope's power plug to bypass the ground. That actually worked for measuring voltage across the resistor!
BUT...I still can't use a second probe, so I might have to stick with the multi-meters. I emailed Rigol, so we'll see what they say.