Steve, the USCG goes by long tons only for displacement and stability calculations. What you calculated is displacement tons. A registered ton is 100 cubic feet and is not a measure of weight. Gross registered tonnage is the space theoretically available for cargo. Net registered tonnage is gross tonnage less certain exceptions and exemptions. I'll be glad to lend you my Subchapter G if you want to go into it more thoroughly, but I warn you(!) that word "theoretical" applies.
In your instance (if memory serves me reasonably well) you should measure the length between the after edge of the stempiece and the forward edge of the transom framing to get "L". Measure the breadth between the inside faces of the side frames to get "B". Measure from the top of the bottom frames to the underside of the main deck to get "D". To do the job right you would be obliged to apply Simpson's Rules for Irregular Areas to account for the rakes and bends in the sides. Then measure the total space in the cabin because tonnage applies to the first deck above the main deck. After all of that you would deduct the space occupied by the engineroom and stairways, the after machinery space and maybe the crew and cooking spaces. The pilothouse would not count because it is above the first deck above the main deck. Other exemptions are mentioned in Subchapter G based on sizes of doors, locations of skylights and ventilating spaces, and so on, and on, and on...on...and...on. If you come up with any number remotely resembling 96 tons of 100 cubic feet you win the leather medal.
The Belle's gross registered tonnage is marked on the main beam, which is just aft of the collision compartment and it is 360 tons. I know because my license is for Inland Waters, steam or motor vessels, not exceed 360 tons with an operator's endorsement for western rivers.