Hi Christian,
After calculating the slope and aspect, the only raster you need to reclassify is the aspect raster. This reclassified raster should be used as the zone raster in the zonal statistics as table tool. The slope raster can be of type float. The result will provide a table with all the slope statistics per aspect class.
I did a test with a larger area of elevation, but the result showed little variation in mean slope per aspect class. Maybe it might be more interesting to focus on a small area or create regions (Region Group tool) and investigate individual areas instead of aggregating all areas with the same aspect class into a single class.
Kind regards,
Xander