Tbh I dont think Distrobox is a senseful way to run GUI apps. It works well as a workaround (firefox, qgis, rstudio, even the Ubuntu PPA VLC) but its slow and bloated.
Mixing GNOME and KDE is a bad idea, no idea what iconset many TWMs use though.
Cosmic by System76 is a tiling-optimized GNOME desktop. And they also have Epoch, which is very pre alpha but will be even better