I think that the first problem here is that your GM has made an error. Fate mechanics give in-system support to the fiction - not the other way around. You said:
My GM prefers to hint things rather than spell them out mechanically,
so I'm unclear on whether the sorcerer was going to fly away,
teleport, hop in a car and drive, or just run really fast.
Which is where I think the problem came from - how is flying away or teleporting an Athletics roll? The GM needed to provide a development in the fiction - something that follows logically from the pre-established conditions - and then apply mechanics to support that development. For example:
GM: The sorcerer presses a hand to his injured face, and as he backs away from you, his eyes dart towards the open doorway to your left.
YOU: I back him into a corner so I can finish the job.
GM: The sorcerer ducks his head, covering it with his arms, and barrels forward, trying to get to the doorway before you can kill him. If he wins this Athletics contest, he'll get past you without being hit again...
In that example, the sorcerer takes a fictional action that follows (who likes being hit with hammers?) and the GM tells you some important things:
- What is happening in the story - important so you can imagine the scene
- What game mechanics are going to inflect into the story now - it's going to be an Athletics contest
- What the stakes of that contest are - IF he wins THEN he is out of the room without being hit any further
You now have an opportunity to respond, showing what happens in the fiction from your end - "I rush him, checking him hard and low with my shoulder!"
When the rolls are finished, you can use:
- Your own Apects (Aging Jock means I know how to hit someone!)
- scene Aspects (You said the old storeroom was cluttered, I'm betting there's Debris on the Floor)
- Or Consequences you just inflicted (He's having trouble standing, let alone running because I just put Staggering on him!)
To influence and re-roll, which I'm sure you know. But the point is, the mechanical influences all follow from the fiction.
So your GM's primary responsibility is to provide a clear view of the fiction - the surroundings, the events, even people's attitudes, etc., as far as your character can know them - because it is from the fiction that all mechanical interventions are drawn, and it is back to the fiction that all mechanical interventions are fed.
And the clear setting of stakes is important, too. Look at the stakes as I imagined they might be set - "he'll get past you without being hit again..." Even if you won, he might have gotten to the door - you'd just have gotten another lick in first! With stakes like that, if the sorcerer had fled, it might have led to a chase through the rest of the building, or it might have led to him getting to a vehicle and maybe a car chase, or a million other options. The stakes let you know how much Fate a roll is worth, right? If the GM sets stakes with more black-and-white conditions - "If he wins, he gets away!" - then you know you can't afford to fail and you'd better go all in. Whereas with my "softer" stakes, you might hang onto some points for the chases and possible resumption of combat you can see coming.
I would talk with my GM about stuff like this - even during the game. GMing is hard! Sometimes, if someone asks for clarification about situations, actions, or the exact stakes, it helps remind me that my players can't read my mind. And it definitely shows that they're paying attention, which all GMs appreciate!