My take is this:
FLA is 120A and I will choose a 150A breaker. A 150A breaker will trip for a current of 230A(191% of FLA) in 400 seconds; trip in 100 seconds for a current of 380A(316% f FLA) and so on. So, at an inrush of 200A, the 150A circuit breaker will not trip the trip range of 400 seconds is enough for your hoist to have normalized its load current.