Can you confirm something? Toolcraft Exemplar can crew a vehicle with crew 3 as long as it's used to crew it during the beginning of combat phase, correct? I think it can but the window of opportunity is small (i.e., not in main phase, and not in declare attackers)
Yes, this is correct.
You’ll have priority in the beginning of combat step after Toolcraft Exemplar’s trigger resolves and you can crew a vehicle with it at that time and still be able to attack with that vehicle that combat.
In a tournament setting, you need to be explicit that you want to act in your beginning of combat step this way by saying something like “Go to beginning of combat and use Toolcraft Exemplar to crew Bomat Bazaar Barge after the trigger resolves.”