I got pulled into a polka with Tracey and Bob at FNW last night, and it turned out to be quite successful. When I've been in this sort of situation in the past, I've usually resorted to a very vertical polka redowa step. This makes it less important which foot you're on at any given time, since you aren't trying to reach and step line-of-direction as much. (And that's important because you can't do 180° turns anymore with three people, so you're always at different angles and you don't have enough feet to handle them all.)
What we ended up doing this time was basically just a traveling basket-hold buzz-step swing, right feet in the middle, paddling ourselves around with our lefts. I didn't think to much about how we were actually accomplishing the traveling, but it seems to work out okay just to aim somewhere and let your propulsion naturally bias itself that direction. We also tried putting left feet in and turning counter-clockwise, but that was more difficult, perhaps just because we aren't as used to doing left-footed buzz-steps.
Another option just occurred to me as well, which would be to mix Newports in with regular polka steps. That way you could remain on a particular foot a little longer, until your rotation has changed so that it's convenient to switch to the other foot. E.g. instead of going 1&2-1&2, you could go 1&2&3-1&2, or 1&2-1&2&3. Obviously you'd be having hemiolas all over the place, and it could be tricky to figure out exactly when to do the switch, and there might be times when neither foot is really convenient to be on. But it might be worth an experiment, especially if you can make sure your threesome can consistently get 360° around every three polka steps.