Hmmm … that is like someone saying he started driving a Tesla a month ago but now bought two 1952 chevy’s without power steering and power brakes.
And it is really beyond me if you have a controller with DJ software why you would ever want to switch to ancient CDJs that don’t even have USB support (as in can’t be used as controllers, nor can they handle USB-sticks) and that can ONLY be used with regular CD’s.
There is absolutely no reason why you can’t achieve your goals of mixing “properly” (whatever that means in your opinion) and “learn my library” (a good plan on any platform) on a controller.
The mixers you mention are either old or very limited in features (like not even filters) or just plain not such nice mixers (my personal experience with the 350 for example is less than stellar).
Sorry to say, but my advice would be to get rid of the CDJs asap and stick with your controller. Spending even more money on limited and/or outdated gear in order to use those two dinosaurs is a terrible waste imho.
The money you save by not buying the mixer and perhaps selling the 800s is much much better spent buying some music and taking one or more of the Digital DJ Tips courses (like How To Digital DJ Fast). With that last course, you will learn “proper” mixing and many other things (including some basic effects use) in less than two months. It will teach you what to practice and how to practice it the correct way to help you avoid figuring it all out yourself and having to go back to relearn things you learned an incorrect way the first time.
Just my three cents, as usual.