I'm not certain there would be a lot of advantage in rewriting the code to use the int*_t variants, but I'm open to counter-argument.
The one place I could see an advantage to changing types might be the fixed_t typedef, as in case sizeof(long) == 64 there would be a lot of wasted space.
I would recommend the specific size types when the actual bit size matters and a different architecture's bit sizes could affect things. fixed_t is definately a place where this is true. Possibly also in bits.c.