Following a mention in a build on a german message board, i took a chance on some new tires.
Italeri # 3890 "trailer rubber tyres" for 1/24 scale semi truck trailer. They have a blank sidewall and a lettered one. Regrooveable 385/65 R22.5
Shove a knife between the Dickie tire and rim to loosen and work it off. Trim the Dickie inner rim bead tire support down to a more normal bead height. Slide the Italeri tires on.
These also seem to have tightened up my turning radius, and now it can climb over a blanket on the floor. Doesn't sound that impressive said that way, but big step up over the hard plastic tires