Tend to disagree about issues with Softride vs regular suspension seatpost.
The only issue we had with Softride on a couple Burleys is when climbing at a high cadence, the stoker started bouncing a bit and felt she was not being as effective as without the beam. Clicked cog into one harder gear and the bounce ceased.
She tried several suspension seatposts and preferred the Softride.
Having said that we have never used rear, or front, suspension on any of our personal tandems.
The tandem feeling wobbly is probably due to inexperience . . . time/miles will cure that.
Wider tires would make a difference, but give yourself some time with the 28s. We now run 25s but for decades ran 23s. Handlebar width is easy to change . . . install wider bars.
Just our opinion/experience.
Pedal on TWOgether!
Rudy and Kay/zonatandem