I'm still researching this issue, but in case this topic is of interest to you as well, here's an update:
Every DROID-, FITS-, and/or JHOVE-based workflow that I have seen thus far can extract PREMIS-conformant core metadata from the WARC container file for eventual packaging with a METS manifest. This includes processing through Archivematica and, presumably, Artefactual's storage-integrated product ArchivesDirect, but we'll see about that one when it's fully released.
Fewer options seem to be available for extracting and packaging the same metadata at the internal file level. Preservica claims to have this extra level of functionality, though they've been reticent to explain in detail how their (proprietary) system works. I'll test it in the near future.
For the moment, the Bibliothèque nationale de France's SPAR Project repository seems to represent the only open(-ish?) source alternative. It runs principally on JHOVE2, but may transition to JWAT-based tools in the near future, and it provides a METS manifest that includes structural mapping tailored to container file formats. This is laid out fairly simply in a 2011 iPRES paper here: http://web.archive.org/web/20150325135508/https://halshs.archives-ouvertes.fr/halshs-00868729/document
It looks like developing this level of extraction into workflows here in the U.S. would take some serious funding and management, but I don't yet see any reason why it couldn't work!