It turns out it's not a tree, but a type of hibiscus called a "Rose of Sharon". Hopefully I'll see it in bloom some day, now that I know where it is.
From there I decided to see if I could find a new wallet, as I've dropped a bill on this trip (someone recovered it for me) and likely did so on the previous trip here as well (though that was not recovered). Mari had said that "Muji" had some good wallets, so I walked to their location in Ginza. They didn't have anything on which I wanted to spend as much money as they were asking, so I doubled back and went to Bic Camera. Where I found something suitable for carrying cards and cash. Because it has the cards next to each other rather than stacked, I've found I can tap the whole wallet as I enter/exit the train station, which is an unexpected plus.
Then it was back to "mouth of the gully" for my only warm meal of the day, then a bit of fruitless hunting for household goods, and then to a grocery store where I bought - among other things I'd missed the day before - dish soap and hand soap.
*By counter-example on the paperwork: I had to register a credit card with the company with whom I'm parking my Canadian phone number. They sent me a form to fill in, but when I explained that I had no printer or scanner and couldn't complete the process, they allowed me to phone in the details.
[We will be] rich in proportion to the number of things which we can afford to let alone.
—Thoreau