By building it this way you would have a belt in the way of the joint 4 rotation. It would reduce greatly the J4 range.

A longer nema 17 with a ratio 1:100 would be a easier solution and would not require modifications and add extra weight to the arm. Since the J3 dont need to more fast I think it would be ideal. Nema 23 might be better if have have concern about the speed too.