Friend,
I travel with multiple ice packs as well to stick in my cooling vest, neck collar and belt and stayed at the Poly LAST YEAR with the same situation.
It is going to be frustrating, I mean like 6 phone calls and 2 days worth of aggravating

, but here is what I can help you with...
Whoever you talk to, which will be several people, you have to tell them you need a "white ice cream freezer". This freezer will be only a freezer, a stand alone and much larger than the fridge in your room. It will only have freezing capability and is very large to fit many packs ( I think I had 20+ last year). You can fit in in room configuration behind the chair and turn the access to the side. THEY CAN GET IT FROM SOMEWHERE. You make sure you say it is NECESSARY because you "overheat, can't control body temp, etc." as that is my case, and don't take no as an answer, they can get one, I believe from the conference center was where mine came from.
((Also, to assume you have issues with body temp....call maintenance and tell they to teach you how to override the a/c because it shuts off when there is no movement! I learned that the first night I was there))
My question to you is have you ever found any really good item (cooler, etc) that will keep packs frozen in the parks during the day??? i have to travel back to the room sometimes twice to switch my packs put rather than being able to take them with me, because they don't stay frozen! Thanks