How could I have converted this draw into a win?


35 f4 looks like it does the trick (if 35... ef 36 Qb7).
You mean Qxb7, right? That indeed looks like a good idea. After that, I would bring my queen back into the battle, or perhaps threaten mate with Ra8. I don't know why I didn't think of it that time :(
Thanks for your reply!