Resampling FIR coefficients
As mentioned in a comment, I would probably try to re-design the filter at the new sampling rate. Take equidistant samples of the magnitude of the existing filter between DC and the new Nyquist frequency as a desired response. Since you want to make sure that the new filter has zeros at integer multiples of $60$ Hertz, split your new filter response into two parts:
$$H(z)=P(z)G(z)\tag{1}$$
where $P(z)$ is a polynomial with zeros at integer multiples of $60$ Hz. Your desired magnitude is then defined by equidistant samples of
$$M_D(e^{j\omega})=\left|\frac{H_D(e^{j\omega})}{P(e^{j\omega})}\right|\tag{2}$$
where $H_D(z)$ is the transfer function of the original filter. In your frequency grid, avoid frequencies at which the zeros of $P(z)$ occur. Of course, those zeros are cancelled by the zeros of $H_D(z)$, but you might nevertheless have some numerical problems otherwise.
Now you find a linear phase transfer function $G(z)$ approximating $M_D(e^{j\omega})$ on the unit circle, and your final filter transfer function is given by Eq. $(1)$.
I would use a weighted least squares approximation, which just requires the solution of a system of linear equations. If the range between DC and $30$ Hz is especially important, you can assign those frequencies a higher weight, such that the approximation is better in that range (at the cost of the approximation outside that range).