OK, this time I:
1. Downloaded FW again, unpacked, and moved to my card (after removing the old stuff from last night). This time it says 16e; the other one said 16. I don't know where I found it, but obviously it wasn't where I was supposed to be looking!

2. Ran the FW update with no cable, and no touching of buttons, and brand spankin' new batteries.
3. Booted up the JBL--Software: v0.16, Patch: v16. So far so good.
4. Connected JBL to PC and looked for elusive .adobe folder--it's hidden, but there! Getting better...
5. Started ADE--got message to authorize JBL...clicked OK...Sucess, I thought. But, even though I de authorized a device last night, I still have too many authorizations. So I have a trouble ticket in with Adobe. It'll be 24-48 hrs until I hear back from the next level of support. Then we'll see if Mohit (the chat agent) explained my problem correctly. Considering he thought I was authorizing an ebook reader on Photoshop

, I don't have high hopes. But maybe I'll be able to get them to let me authorize at least this JBL without losing my PB360 in the process.