Thanks, Steve, Petey, and DrQuackner!
DrQuackner, you’re right. It will only roll forward and backward. I hope I never need to move it sideways when it’s loaded, but you’re right—if I do, I’ll have to drag it.
My initial inspiration was the wheels on my wife’s elliptical exerciser. Its wheels are concave and ride on tubes. I thought some like that would be perfect to keep the rack from veering into the wall and scratching it. I couldn’t find anything like that in my brief web searching. (Even if I had, I bet it would be expensive.) so I chose casters.
I had planned on capturing the casters against the wall in a track formed by two parallel boards (with a front stop block to keep the rack from reaching the sink). I’m not sure I’ll need it, though.