Green flame Blade can't be twinned
For a spell to be twinnable it needs to only target one creature. As clarified in the PHB errata:
To be eligible, a spell must be incapable of targeting more than one creature at the spell's current level.
Green flame blade is able to target two creatures; the one you attack and one next two it. (See also developer tweet on the matter who agrees with this.) D&D 5e does not define targeting as well as it maybe should. If you would like to read more words on this and/or argue it, I direct you to the questions What counts as a target for a spell? and ask you not to argue it in my comments.
The rest works
To go through the logic: Green flame blade requires you to attack with a weapon you are holding and shadow blade explicitly creates a weapon (as opposed to say flame blade). There is also no limitation on casting two cantrips per turn, only to casting a spell of 1st level or higher on the same turn as casting a spell of 1st level or higher as a bonus action.
This may be efficient, but it isn't majorly broken though, it's costing you a second level spell (which you have to maintain concentration on) to set up and two sorcery point every turn (to quicken the cantrip).