Not knowing what your system currently consists of, but if you’re willing to look at used gear, the McIntosh MX-120 has a nicely integrated variable loudness contour that provides more control than an on/off loudness switch, allowing you to dial in to compensate for the FM principal.
The unit was marketed as home theater processor, but 2-channel analog side of this unit is essentially a C48. It would solve your problem, but would require the purchase of a power amp if you’re coming from an integrated.