How can I look for another job while I am actually bound by current job working hours?

The "in-person" route is the best way, like you've said, but since your boss is inflexible, you may need to take your personal days to get it accomplished. I don't know how many off days you get, but you need to treat them like work days, because finding a job is WORK. If you don't treat it that way, you won't find anything. So apply that work ethic you already have to finding a new, more exciting job in your unoccupied time.