You were exactly right. I installed Essbase Server under an installation id (which they took from me) and EAS client under my own id. The patch util and the install tool only see EAS because I'm running them as me, too.
I found files called .oracle.products in my own document directory and that of the install id. Of course they had differing information. It's just XML and not too hard to understand, so I merged the data and saved the files back to both directories.
I re-ran "create inventory" and the patch util seems happy now. It's running, anyway. I'll let you know if it succeeds.
Thanks a hundred,