You added most of the nameplate values in an edit, so that will help with people getting you answers. But you need to clarify the heat pump and airconditioner situation. A heat pump usually provides both the heat and AC, so is the AC a separate one or is this just the compressor part of the heat pump? You also need to know how the air handler is setup -- can all the resistance heat in it be used while the compressor is running, or is part of it locked out? If you don't know, assume that all the strip heat and the outside compressor can run together. Is there a nameplate on the airhandler indicating MCA, or FLA and heat KW? We also need the nameplate value for the compressor portion (which should be listed as MCA or RLA+FLA). You could guess 18 amps for that, but you shouldn't guess as the values can be all over the place.
I don't understand your inspector's 125% comment. Residential services rarely have anything that is continuous, and its those items you multiply by 125%. All the standard calculation mandates is a 25% increase for the largest motor you have and that's it. But having a 25% growth margin is probably a good design.
My rough answer, based on what you've provided, is: 164 amps
I assumed the heat pump was 46 + 18 amps at 240V, that the disposal was the largest motor, and that the water heater, disposal, dishwasher, attic fan, and microwave could all have a .75 value used because of 4 or more fastened in place equipment items.
A 200A service should be perfect for this situation unless they plan on adding a hot tub. For most installs, the next size up is a 320A meterbase and a second main panel (a 300A or 400A service), which causes a substantial price increase.
