SteveJ ... why not make a jig for use with a drum sander attachment on a drill press? You could even turn custom sized drums with your lathe and attach sandpaper of whatever grit you wish!
I'm a complete newbie with this sketchup toy, but it only took me about 10 minutes to throw a rough picture of what I have in mind together .... (side note, sketchup is kinda fun!)
The flat base can be clamped directly to the drill press table ... the smaller wall of the jig can be mobile, to accommodate different thicknesses of original stock, though making it one size to fit what you're pulling off the bandsaw or tablesaw makes it much easier to use ...
You could also set up a featherboard on the opposing side to help guide and feed the stock in one direction only, or opt for a featherboard in front where the shorter wall is instead. It would probably be safer, too! That and I think a featherboard would be easy to make adjustable, if need be.
Set the thickness by clamping the jig down where the large back wall will be the right distance away from your sanding drum.
Don't forget to make a push stick of the correct thickness to be able to push your stock past the sanding drum!
