Oh man, I fixed it!! I posted earlier I had phantom tabs showing up on my new iPad Pro from my three existing / "rogue" devices. I wasn't quite up for the task of signing out of iCloud and removing them from my Apple ID since I would have needed to do it for each of those three devices. Plus, I didn't want to run the risk of potentially introducing new issues, or setting up my cards in Apple Pay again, among other things.
Searching the web about this issue indicates that an Apple support page apparently used to state "If you can't access the device that shared the tab, the tab will automatically be cleared from the list after 14 days if the tab isn't updated."
I was going to wait a couple weeks to see if they would disappear on their own even though I still had my devices, but then I thought what if I just change the date on my iPad to the future? So I did just that. I set my iPad Pro to July 1st, opened Safari, and BOOM...the phantom tabs were gone! I set the date back to the current date, they're still gone and the correct ones are still showing/working.
Obviously YMMV, but this may be another/simpler option to try rather than signing out of iCloud if you have phantom tabs (or just wait a couple weeks). I do realize some people don't like changing the date, but I've never had any implications from having done that several times in the past for other reasons. I figured this was worth a shot before trying other things that would have been a bit more involved.