Welcome to the Forum...
You're good on your calculations. Inrush might pose a problem on your 200 amp breaker. You might see if it has adjustable trip.
alos make sure your HVAC isn't 480. Since it's an existing service, the HVAC may have already been spec'ed.
If you have restaurant experience you don't need the next "not asked for "advice, but if it's a first....before you get in too deep, get an equipment schedule. Since you apparently don't have a print, it looks like it may not be a "designed" restaurant and those folks are notorious about "picking" equipment and you end up with multiple voltage/phases, etc.
You could probably get a number of horror stories from Forum members.
At my age, I'm accustomed to restaurants asking me to pay in advance, but now my bank has started sending me their calendar one month at a time.