I have a Puma Cobalt 5000 which has a lot of concaving. Maybe talk to someone at Rob Pack Cricket?
You can pick up wooden coffin planes on eBay. They will be flat bottomed but all you need to do is radius the bottom yourself. Can be done with a spokeshave and a machine sander and then match the blade to the shape. The blade will need grinding and re sharpening but it's worth a little effort. Pretty cheap tooI have both round bottom planes and travishers. I use travishers for removing the wood and the round bottom plane for fine tuning.
This might sound like a stupid question but if I was to round the bottom of my coffin plane that I have, would the fact that the blade is straight not mean that I will end up taking huge slices out of the wood and having a really poor finish?Is it possible that you could post a picture or two to explain a bit better?