Currently there is no way to add a custom creative menu, but you could always give yourself the new items and save them to a hotbar, just look up creative hotbar saving and you'll find out how to do it. It would mean you'd need to give yourself each item once, but it's better than doing it every time. I personally use it quite a lot, being somebody who makes datapacks, it's really useful for me to have quick access to my custom items, so I started using the quick hotbars and it's been a brilliant time-saver!

The closest thing would be saving the custom items to a toolbar

Unfortunately, no. It might be possible to add it to JEI using configurations (but only if you play with JEI).