You are responding to a post that is five years old.Its a good question but seems a little bit tough to answer. However arguing without pointing any valid answers is an easy way.
According to my perspective view- " You cannot apply now without valid poof of residence, but In order to get any, the shortest time for- bank statement - 1 month as you said, or else get a G1 license in short time (not recommended for your case). Mostly by 3 month after landing, everyone will find any valid proof of residence to produce. Apart from this 3 months, there is a waiting period of another 3 month for OHIP card. So total 6 months would be the max time period in worst case in my suggestion. So better be ready with any Private insurance for the said period."