Resampling sharp Foveon images

As you said the solution is up-sampling before any operations are done, and in the end don't down-sample, just keep the image size. That's what's done to satellite imagery, planetary imagery by probes, or any other field of science where images must be geometrically corrected but all the information is precious.

Upsampling 2x is more than enough, and even 1.5x is ok if you use good algorithms after.