The HR-24 uses exactly the same codes as the HR20, 21, 22, and 23. So take your pick. Even if the 24 turns out to be in the database, I'd recommend the HR20 codes instead since they're known to be correct and complete. HERE's
how to add some extra HR2x commands which aren't in the harmony database and probably never will be.
You can likely use an older Toshiba code set for your new TV as well. Just do a little homework and pick a recent similar model (doesn't have to be LED). If that doesn't work (I'd be very surprised if it didn't), then learn them. Post back if you need the pronto hex for discrete on/off and discrete inputs. Logitech support can add those for you.
Guess how new devices get into the logitech database. Bingo. Users like you learn them and do all their work for them. I've learned plenty of devices for my harmony. It's tedious, but not difficult.
Bottom line is any harmony, including the 700, will work fine.
Getting OT here, but the HR-24 actually comes with a very cool remote. It can actually download codes from your DVR and upload its config back to the DVR. So if a new device comes along, you can pick it from the screen on the DVR which then beams it to your remote (via IR, I think, the same way we JP1ers have been downloading/uploading from/to other UEI remotes via cables and sound files for years). Then your remote beams it's config up to the DVR, so if you ever get a replacement, just download the config and you're back in business with all your codes. Kind of a poor man's harmony, only wireless and macro-less (except for one). That being said, I'd still rather have a serious universal with at least learning and macros. But if your needs are simple, the new DirecTV remote isn't bad.