I'm not sure if it'd work or not, I'm just throwing it out as a possibility to consider.
I do know that -- by repute, at least -- the DC offset issues with ring- diode DBMs is due to the LO getting into the signal. I'm not sure if they are, or can be made, inherently better than Gilbert-cell mixers or not.
Come to think of it, whatever you use, if you can periodically cut off the signal to the mixer you can measure the DC offset in "quiet" mode and null it out automagically, then go back to your regularly scheduled programming.
If I did that I'd have it going on all the time, which means that (a) my intended signal would be getting well chopped up, and I'd have to deal with it, (b) I'd need to capture the DC bias well and often, and (c), I'd have to pay close attention to settling.
But it might work.