I usually don't answer my own queries, however we have found a workaround and I wanted to share this in case anybody else runs into the same quandary.
1. Run REST API method "add tags to workbook", but add a dummy tag such as "zz_dummy". This will add tags to each individual view.
2. Run REST API method "delete tag from workbook". Delete the dummy tag. TaDa, now the remaining tags are attached on the workbook level too.