My question looks rhetorical but it isn't. I am forcing myself to write to-do lists and tracking what I've done, but I found it difficult. I get bored to write lists longer than 10 tasks, so I set general tasks that never get done, and my list is becoming cluttered and ineffective. In this period I have a lot of overdue work, that's the reason of my cluttered list and of my need of organization. Is there any established method which requires minimal logging? GTD does not look as the right method for me, unless I can find a "perfect" tool
The reason you don't like GTD is because you are not even trying to do GTD:
Don't force yourself to get a whole to-do list at once, but re-iteratively improve it.
Here are some tips that match your points above:
Looking for less logging and tracking is definitely not the way to go, it defeats the purpose of trying not to use your mind to keep track of tasks you should not forget about. Write the tasks down until you are bored then split them up (in multiple tasks, contexts [using tags] and projects), then you should be able to progress through them with ease.
Still not OK?
If you set tasks that never get done, this could mean that these are things that you don't really care about (and you maybe don't need to do them) or are poorly defined: I once stumbled over some really old tasks and wondered why these were so hard to do: They were not a proper instruction what to do, but rather something like "think about $complex_project". After I split them up in several subtasks and defined a proper next step it worked better.
You may have noticed, that I used some GTD terminology/methods there: This is because I use a subset of GTD tools and omit some which I don't find useful for me: I use the concept of one central place to store tasks (for me it is Taskwarrior, a command line tool) and I try to make sure that ever project is split in manageable subtasks. Reviewing the task list on a regular basis also does not hurt.
When I have problems similar to what you describe, I step back to look at my GTD system. I almost always discover the problem is caused by one of two things:
In GTD terms, a Next Action is a very carefully defined thing, that must result in a concrete deliverable. A good NA (to piggyback on one of the other answers here) will be "draft project plan outline for $complex_project" or "draft candidate design for $complex_project" rather than the general "think about".
And staying with GTD terms, you don't need every possible action for a Project in your list(s). Just the next action you need to take to move the project forward. When you have completed that action, it is your choice whether to proceed with the next thing to do with that Project, or to move to something else on your lists, or to process an inbox.