Thanks for the update started working?Haha, replying to my own question, but maybe it will be useful for somebody)
So I went to Service Ontario today, and was told that I have two options: 1) to apply for OHIP after I get AIP letter (no need to even show work permit, it's irrelevant in this case); or 2) to get the letter from employer stating I work full time and they intend to keep me for at least 6 months (you can check the guidelines to the letter on official OHIP website). Having case 27 on WP is not a problem at all. Also, the 3-months waiting period starts from the date of employment. Seems quite easy)