This much of your sentence is fine:
It is really a very simple change, minutes, and I want to pull it in soon.
When a comma serves two roles, such as the one after “minutes”, they are merged. If one had been a colon, semicolon, period, exclamation mark or question mark, that would take precedence:
It is really a very simple change, minutes; I want to pull it in soon.
However, you do have a problem with the third comma:
I want to pull it in soon, since it is an annoyance.
When the subordinate clause follows the independent clause, you do not use a comma:
I want to pull it in soon since it is an annoyance.
You only use it when the subordinate clause comes first:
Since it is an annoyance, I want to pull it in soon.