The committee does not need the involvement of the SM to call a SC meeting, nor for that matter any other meeting.
You seem to have the gist of what’s required to call a meeting. I just add that you need to display the meeting notice on the notice board, OR you need to send a notice to all owners.
The minutes need to be taken and published. There is no prescribed form of the minutes, so as long as it’s an accurate record, it’s fine.
And the committee can only resolve matters that are contained in the notice of meeting. You can discuss anything else but not make resolutions.
The secretary is the person who should send out the notices, but anyone can do it provided the secretary puts their name at the bottom.
Normally the Chairman of the OC runs the meeting. In their absence the members present can elect a chair for the meeting.
What you are suggesting is not unusual, and you should be commended for taking such action particularly where the SM is dragging the chain.
And the final word, the SM is not required to be at the meeting. Sometimes they want to be there just to collect their attendance fee (depends on your management contract).