The price jump was probably legit, and I'll explain why. Rekeying only works if the cylinder is healthy. The locksmith pulls the plug, swaps the pins, cuts you a new key. But if the cylinder itself is cracked or the internal mechanism is shot, there's nothing to rekey. You can't pin a broken lock. At that point the only real fix is a new cylinder, and that's a different part cost and a different job. So no, rekey and replace are not the same work, even though they look similar from the outside. The mismatched hardware thing is real too. It's way more common than people think, usually because someone before you replaced one side with whatever the hardware store had that day. When the outside and inside halves are from different manufacturers or different generations, the screw alignment, the tailpiece, and the mounting holes can all be slightly off. A tech can burn a lot of extra time fiddling with that. I've opened up doors like that and just stood there shaking my head at what some previous owner glued together. Where you might have pushed back is on process. A fair locksmith gives you the new price and waits for your ok before touching anything, especially on a flat-rate quote. Once he saw the broken cylinder, he should have said something like 'this can't be rekeyed, replacement runs X instead, want me to proceed?' If he just did the work and then told you the number, that's the part I'd have an issue with, not the price itself. Also worth asking for the old cylinder back. Some guys keep the old parts, and you want to see what he pulled out. If it genuinely looks busted, you got a fair deal. If it looks fine, that's when you call and ask questions.
As for handling it in the moment: it's ok to say 'hold on, call me a price and I'll decide.' Worst case he packs up and you pay a service call. Late at night with a shed you can't lock, most of us just pay. You weren't dumb, you were tired.