Would it be possible to port (part of) your package to modular arithmetic with machine-sized prime numbers, for number-theory purposes? (See e.g. Linbox C++ library.) There is not yet a Julia library in this niche area. Since your code can handle generic numeric types, I imagine the only change needed for modular arithmetic is that pivots should not be chosen based on magnitude of a number, which is not defined in finite fields.
P.S. of course, BLAS routines, if used, would only work for floating point types.