My idea is a bit impractical, but hear me out.
I am assuming you're doing this all within an event. It looks sloppy to reprogram your fixtures during an event. I'm sure your guests won't give a crap, and that's fine since that's all that matters anyways.
My suggestion involves doing something that you're normally not supposed to do.
I am suggestion a second pair of the units. Put one pair with DMX, use with the controller. Use another pair as master/slave, and then turn them on/off via a relay/switching pack. You shouldn't run these off a switching pack because you can damage them or at least the chance of damaging the lights is greater than average. Using a switching pack tends to help. Even so, it's still not recommended, but it COULD be done.
I think you'd be best off having a DMX controller of some sort and then an UC3 for the other pair.
So, you want to eliminate the cheese but keep the look. OK, not bad.
If it was me, I'd find a safe way to switch pairs safely, even if it meant having a power unit with remote turn on/off, which is most likely how I'd want to go. But I ain't going there yet.