First off, punctuation is your friend.
Very hard to read your post but here goes: Unless there's an opening in another workcenter, you won't get far.
You might talk to other TLs about training in their areas so you can be 'global' (also helps you get more hrs).
If you've helped once or twice on SF, see if you can pick up shifts from the swap board.
These are opps for you to shine so you'll be noticed by other TLs who, in turn, will want you on their team.
We had several stellar CAs but they almost always got snapped up by other depts.
You might also talk to your ETL-GE about getting more than just closing shifts.
If she doesn't budge, you might talk to your ETL-HR but your better bet is to get noticed by other depts.