Bathroom joist analysis and strengthening plan for remodel

We are remodeling our master bathroom and have removed an old jacuzzi tub and vanity. We are planning to install a 66" cast iron pedestal soaking tub (see spec) and a new vanity (see attached pdf). The vanity is drawn in the pdf but the tub is not. The joists are 2"x10" yellow pine on 16" centers spanning about 14' perpendicular to the tub and vanity. The tub will be centered on the center of the outside window with the center of mass 21" away from the window/wall. The tub specs are attached. The vanity is 6' by 1'11" with a leg at each corner supporting the weight. There is a joist centered on the window under the tub (so there are 3 joists under the tub) and 4 joists under the vanity. We've done a basic analysis use tables and the loads are too much. We need: 1. A joist load analysis and modification plan to ensure the weight of the 400lb tub plus water plus person plus the 400lb vanity will meet code and be structurally sound. There are 3 joists that are sustaining the load from all of the tub and at least half of the vanity. The dimensions of the bathroom are on the attached pdf. There will be a tile floor installed. 2. A plan on how to strengthen the joists. We expect to have to strengthen the joists as they have been cut during original construction for the original tub drain to a point where I don't think they'd meet code. We can't sister them the full length as they extend under the bathroom wall to a first floor wall. We do have access from below as the drywall ceiling has been removed from the area below the tub and vanity due to a water leak that we are repairing. That means we can sister and block as needed. We may need a PE-signed document but at this point we don't think it will be required. We do need the detailed analysis in case we get challenged by the building inspector. We are our own contractor, we are doing the work ourselves, and have the building permit under our name. You would have no liability for the design. If you need more information (measurements, masses, etc) please contact us.