I would say you are correct. Get the swap broom first then defeat all of the other bosses in the quickest order. And yeah, you would have to defeat Briar, either saving it for last or beating it first after getting the swap broom.
I don't know who wrote the 100% definition list. I define 100% as all cards, all hearts, all keys and all upgrades, which include boots. I saw it as having every slot in the menu filled, all the basic game cards and the unlockable items.
I don't think I could handle a glitchless 100% run, seeing how long the glitchless any% is. And the bonus cards/items don't count towards 100%, so you could easily do it glitchless. It's just a lot of running back and forth.
I'm sure if you record the run and put it up they would find a spot for it. Not very many people run this game so the more the merrier I always say. Good luck with the run!