If you want simpler, then you can export DICOM. Unfortunately the DICOM SEG exporter is currently broke, but very close to fixing, see https://github.com/QIICR/QuantitativeReporting/issues/140
Exporting the segmentation to the labelmap takes around 8 clicks additinally to the few hundred you made when doing the segmentation. I think it is still much simpler than coming up with an elaborate workaround. If you want to make it quicker you can always write a python script that does that for you.