This link has some background info on tandem tire selection:
You folks are a relatively light team at 275 lbs, so you could easily go to 28mm or even 25mm tires *depending on your rims*. As the linked page points out: "Use of a narrow 25 mm tire on a fairly wide rim common to many modern tandems such as the Velocity Dyad or Chukker models will unnecessarily expose the sidewall to road debris and the lowered profile increases the propensity for pinch flats." On their current model Galaxy Twin tandem, Dawes uses the Alex DH19 which are 24.6mm wide. This compares well with the Velocity Dyad at 24mm. So if your rims are similar, I'd think you would not want to go smaller than 28mm on the tires. If you're going to ride on gravel or mud more than very very occasionally, you might want something a little wider to give you more comfort over the bumps. But if you're on the road 99% of the time, I would think 28mm would be fine.
I was not familiar with the Dawes Two-Way Street LadyBack, so I searched quickly on google -- looks like flat bars, triple crank and cantilevers. To your comment about it not being a road bike, you could easily put drop bars and brifters on it if you wanted to.