The north pole tool in FT is for rotating the fractal function. It doesn't do the editing data primarily because implementation limitations don't guarantee that reprojecting the editing data is reversible: if you change your mind, the system can't get back the exact input data (and then I'd get to hear "FT destroyed my data", which is not particularly fun). There could be an extra and expensive reprojection step at every sampling operation, but that would slow things down significantly and FT is plenty slow already.

If you're interested in keeping altitude data, you can output the raw altitude from FT as a Special MDR file (an Equirectangular projection raster with a 1024 byte header and little-endian floating-point values). This file should work as an input to something like one of the GDAL tools (probably gdalwarp) provided that you use an appropriate VRT file ( see https://gdal.org/drivers/raster/vrt.html for info on the descriptor file needed). There is probably some way to get it to work in a single step, but it might be easier to reproject the image into two Orthographic projections, one centered at the desired pole and the other on the opposite side of the world. Then reproject those two images back to equirectangular, specifying the Orthographic projection's centers as poles. It's not a simple process, and I expect that there are tools out there that will do this in one step (it's making sure that it works with the altitude data and not RGB images that's the hard part). After the map is fully reprojected, it can be put back into FT using File>>New with type Binary File.

I would generate a script or program to do this process directly, but I don't have the solid block of time available at the moment, sorry.