"I composed music over the last twelve years, but almost quit for many
reasons"
You are right about past simple sounding awkward here. "over the last 12 years" means the 12 years up to now, which means present perfect or past continuous (was composing) can sound more natural (past simple in the first part is okay, but would perhaps be better with "for the last 12 years").
Further, you indicate that the action of composing is not completed: you have almost quit, but you never actually quit, which contradicts the use of past simple.
(It is possible to use this construction [with minor changes], but this requires a very specific circumstance - if you are a recently retired composer, for example).
"I have composed music over the last 12 years, although I almost quit
(once/a number of times/two years ago) for many reasons"
sounds perfectly natural, but means that, as of the present moment, you still do compose music. (Note the time markers; without one, the "when" aspect of quitting is left in the air).
What you perhaps want to say with past simple is
"I composed music for (the last) twelve years (but quit for many
reasons). Now I just play songs on my guitar".
Here, the action of composing, which lasted for 12 years at some point in the past, is completed.
The present perfect is not permitted with ten minutes ago.
As explained here, the present perfect is a statement about the present, not about the past. Consequently it cannot be used with temporal expressions located entirely in the past, only with temporal expressions which include the present.
Ten minutes ago locates the departure in the past, and therefore requires a past tense. Since the departure was completed at that time, not continuing, a verb in ‘perfective’ aspect is required; in English, that aspect is expressed by the simple past.
Best Answer
"Just now" makes a more explict reference to time. It means the immediate past. It tends to get placed, like other time references at the start or end of the sentence. And it means "in the immediate past". As a time reference it would happily go with with a past tense verb. "I went shopping just now".
On the other hand, "just" is placed between the auxiliary and the participle "I've just gone shopping". You can't place it at the end "*I have gone shopping just." It isn't acting like a time adverbial.
But these are only at most tendencies. It is quite correct to say "I just went shopping" and "I've gone shopping just now."