I didn't answer all of your questions.  Sorry.  PoserPython can't create a group, so no, the groups wouldn't be retained, using the earlier approach.  They could be inserted back in afterwards, using a geometry insertion pose (which would basically have to contain the whole formatted OBJ).

The approach in the attached script might be altogether more promising.  This will trim a prop, once again using the SQUARE as the bottom definition.  The prop to be trimmed must, in this case, have an empty group named "NewGroup" (without quotes) added using the grouping tool, before the run.  The script fills that group and spawns a new trimmed prop from it.

As noted above, a pose can be used to insert new geometry, and hence new groups.  I'm going to see if I can work out a simple extension of the attached script which creates such a pose for the NewGroup, so the grouping tool doesn't need to be included.

But it looks like that will have to happen tomorrow.  I can hear a thunderstorm approaching, which means I'll be off the computer until it's over....

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Cage can be an opinionated jerk who posts without thinking.  He apologizes for this.  He's honestly not trying to be a turkeyhead.

Cage had some freebies, compatible with Poser 11 and below.  His Python scripts were saved at archive.org, along with the rest of the Morphography site, where they were hosted.