I think that the results are "folklore" in the sense that if you have no concern at all for numerical stability, using small translates of the Gaussian to obtain derivatives is the first thing that you'd think to do. Likewise with the trig functions with frequency $\omega \ll 1$, you can just directly differentiate many times with respect to $\omega$ and then evaluate at $0$. You get polynomials, which are dense by the Weierstrass approximation theorem. You say several times in the paper that the results are surprising, but in my opinion the qualitative results are not all that surprising.

These results are at least similar to popular results that certain sets of wavelets are bases, and certain other sets span but are overcomplete. I don't have a reference, I just remember hearing about a set of wavelets on $\mathbb{R}$ that comes from a general lattice in $\mathbb{C}$. Whether the wavelets span or are overcomplete depends on the determinant of the lattice. This is not the same result, but it is similar.

Your paper also analyzes the numerical stability of your approximations. That seems like the more original contribution to me. Maybe the referees would be happier if you shifted the emphasis of the paper to the numerical stability issue.