Euge,
I have two Brownie Hawkeyes that were built for 620 film. One won't handle 120 film no matter what, respooling included. (I modified it for 35mm.) The other works fine with 120 film, out of the box, as long as I use a 620 take-up reel. I have a metal 620 take-up reel that I use with the camera and I have several plastic 620 take-up reels that I have never used. If your search yields nothing, then send me an e-mail with your address and I will post a plastic 620 reel your way.