Yes, narrower tires could be the answer. Bearing in mind that there are certain types of snow that clog up all snow tires, even if they're on a dump truck, in general, narrower tires try to sink down to the pavement where wider tires try to float on top.
I ride an all-weather off-season group ride and on that ride, I've seen just about every combination of bike, tire, rider and riding surface. Everyone has troubles at some point. There is no "best solution" for all circumstances. There have been times when my 35mm Nokian Hakkapeliitta W106s have worked better than other riders' fatties. Then there are times the fatties work better than my Nokians.
From what I've seen on that ride, in my commuting, narrower tires are better, more often for the conditions I usually ride in. That's a lotta qualifiers, I know. But as a seasoned snow commuter, you also know how different conditions can be in the space of just a few feet.
The best advice I can give is to think back to the times your fatties seemed inadequate and ask if a narrow tire would have found traction if it had sunk down through the slop. When you find yourself thinking that more than half the time that's true, think about skinnier tires.
Or, you seem to have the good fortune of having two types of bikes for winter use. Put decent studded snows on both and switch bikes depending on conditions. You'll sort it out for yourself PDQ.
I don't know if I'm in the slop more often, it's just that I tend to be in it when I'd least prefer to dump my bike, - when I'm in traffic.
I have two bikes period ;-)
The MTB used to be my nice "new" bike until it spent the last few winters on the road. Now my "vintage" road bike is the nice one just because nothing's rusted on it. It's tempting to use both this winter to see which setup works best or to have different choices depending on the conditions, but geez, I'd like to have at least one nice bike come spring instead of two overly oxidized beaters.