Mark
-How big is this slab? If a floor sander would work, it must be fairly large
- How much do you need to take off?
If a belt sander is too slow for you, I would have second thoughts that you'd be happy with any type of a pad sander. A belt sander with the right grit, can remove material fast.
Hand power planer can mess up some wood really, really fast, if you're not careful, and you'll still end up with a sander in your hand.
I know you don't like the router sled, but if you look at the geometry of a router, "bowl bit", there is no hard edge to catch. Used on a light climb cut, it may be a possibility for you. Any sanding solution, other than a machine powered sanding option, is going to be slow and tedious.
"The first thing you need to know, will likely be the last thing you learn." (Unknown)