I understand you don't want to use FGDBs, but in this case, does it necessarily matter? The reason I ask that is because the data is going to be stored in AGOL, regardless if you use a FGDB or shapefile. So you could temporarily use the FGDB to enable GPS metadata, then publish to AGOL and then at that point you wouldn't need your FGDB (or shapefile) at that point.
Then, the data would be collected in AGOL/Field Maps, and you would have the option to download the data as a shapefile (which would contain the GPS metadata fields).
Besides this, I'm not sure if it's even possible to enable GPS metadata on a shapefile.