  Using the theory of noncommutative geometry in a braided monoidal category,
we improve upon a previous construction of noncommutative families of
instantons of arbitrary charge on the deformed sphere S^4_\theta. We formulate
a notion of noncommutative parameter spaces for families of instantons and we
explore what it means for such families to be gauge equivalent, as well as
showing how to remove gauge parameters using a noncommutative quotient
construction. Although the parameter spaces are a priori noncommutative, we
show that one may always recover a classical parameter space by making an
appropriate choice of gauge transformation.
