I just wanted to clear my part of this up. We all know, and hopefully the OP knows, that bringing current to the red wire cannot be from the same buss as the black. Said and done. What's left is the possibility of a MWBC. I did not know that was possible to an outbuilding. Then other possibility is a 240v supply to the existing panel in the garage. This is depending on the existing wire size. No point in doing 240v on 12 ga. or less as providing branch circuits in the garage would be limited to that which can be done with, say a 20 A MWBC on 12 ga. IOW, no ability to have both 120v individual circuits AND a 240v circuit in that existing panel unless the wire ga will support that.
Seems like the discussion did go 'off the rails' a bit but it's been an informative thread.
Now we must get down to brass tacks and determine what exactly this "armored cable" has AFA wire gauge.
And since the OP is not likely to change out the fused circuit to the garage, talk about tandem and quad breakers is moot.
One more thing: looking at Post #1 and the pics, I don't see how 3 breakers in a row on one side of that subpanel are all on the one leg. What am I missing there?