It's been tough for this November too and was last year as well. Don't forget it's not only the only HS character meal, it's also the only Disney Jr character meal at all.
My kiddo got sick last year during our meal there (ugh it was a nightmare!) and missed seeing Jake and barely saw Sofia and Doc. The CMs fortunately remembered us 2 days later because even while at WDW, NOTHING opened up even with paid search, plus my constant searching, and not even anything for our hotel concierge who kept trying. Luckily, a manager there at H&V was able to squeeze us in (I called and thought we were going to be allowed to just be able to take a quick pic with each character but she arranged a table for us which was an amazing surprise!), but every time we have been there waiting for our table, they turn several other families away.
People have told us years ago they used to show up for a late breakfast or lunch and were able to walk in (or try to go on a list at 8 am and were told to check back around 10:30 or 11, but with Doc, Jake, and Sofia (poor Handy Manny, he's so sweet), there's no openings.
So if you see a time pop up, grab it. Also remember there's no characters after 4. We've seen people that didn't realize this each time we've been.