One step further. Sure, it's possible she likes guys fighting over her. If that's so, you are advised to stay the fuck away. That goes for anybody; if your romantic interest of the hour seeks the attention of multiple people for the express purpose of those people fighting over <appropriate pronoun here> then do not even think about entertaining the idea of being one of the chumps in the ring.
Anyway the friend zone is an informal conceptualization for an area where guys end up in a woman's mind that essentially defines the guys as "good friends, not viable romantic partners." Pro tip, you do it too, don't pretend like you don't. It's not that being friends *innately* makes you less likely to be dateable, it's that you, at present, are a friend who is not dateable. Sorry, hate to piss in your Cheerios, but that's where you are right now. The bear hug isn't childish, but think about what it is. It's a bear hug. Who gives bear hugs? Teddy bears. Big teddy bears. You have classified yourself as a big teddy bear. Who dates big teddy bears? The occasional objectophile. That's it. Not anybody you're interested in dating, in all likelihood (and my sincerest apologies if you are in fact an objectophile OR seeking one).
The correct response is that she's not interested in you right now, and that you should proceed as friends if she's worth friendship (tip: if you want to date her, you better want to be her friend, because in a healthy relationship, romantic partners are, if not one another's absolute best friend, certainly up there), and if not, then (a) what were you doing going after her anyway and (b) step back and reassess.
Also if your half-friend/half-business-associate is leaving for good soon then just chill out and wait. For one, that'll probably improve your odds *if* you nonetheless feel the need to plunge down this rabbit hole. For another, it's just basic decency and respect, man. Presumably you're looking at making a move because you anticipate them breaking up when he leaves. Just set this thing on ice for a while, keep living your life, being you, whatever, and if it does come to pass that she's single in the near future, and you *really* think you have a chance, go for it. With less bear hugs.