Unfortunately I think a lot of what you're going to want to work on is going to require you to go to a school, for several reasons:
- The simple fact that I don't think training on your own will count towards time-in-grade (unless you already have that)
- When training by yourself, you typically gain muscle memory in what you know, but don't get the critique to fix problems you don't even know you have. That's why you go to class and train at home, so you can get feedback and figure out what to work into muscle memory next.
- Training by yourself is incredibly difficult to train your timing and distance for sparring. At the very least you want another person holding pads so they can move with you, and at best someone to spar with.
- As you move higher up in rank, it's going to be more about what you can do for the art. You should be working on things like mentoring lower belts, practicing with your peers to develop your skills, coaching students in tournaments, judging belt tests, and teaching classes. Maybe not all of those things, and definitely not all at once, but these are important skills too, and you can't really practice them on your own. Now, leadership skills are maybe not required for 2nd Dan or even 3rd Dan, but by that point it should definitely be on your radar.
- When you train by yourself, you have no support group and no accountability. It can become a chore without a purpose.
My recommendation is to not restrict yourself to Taekwondo. If there aren't any schools that you like that you can attend, try finding a school in a different art, or a different discipline entirely. For example, skills you learn in Karate will help you with your Taekwondo skills. Skills you learn in Brazilian Jiu-Jitsu will round out your martial arts. Or dance classes can help you work on body control.
A black belt who is still going to class would get feedback on what to work on. One who has not been to class in a long time might not realize what needs the most work, what mistakes are being made, or what the best way to fix them is.