After digging into Sitefinity more, I think it would be more appropriate to create custom catalog and order providers, but I cannot find any documentation or blog posts about doing this. So, I've started to try to figure it out on my own (and will blog about it when I get it working).
Is CatalogDataProviderBase the correct class to provide Sitefinity with catalog data? I've tried to implement that, and created a provider entry in Sitefinity catalog settings, but the methods of my provider type are never invoked. What am I missing?