I had to add the extended object into my Component Template for the data to appear. Then discover and snap as usual.
You should not have to. the etl will bring over asset-based data (actually for the asset-based snapshots there is a hidden template named after the job)
I should have updated the post. The issue is a defect in fact, so I wasn't crazy. There's a hotfix available to enable loading of EO data in the ETL in BSA 8.5.01.304.
See QM001870669 for details.