60dB is certainly not too much gain for a 0.4mV cartridge. That nets an output of 0.4 V, which should certainly not be overloading anything within the phono stage or downstream of it. Something else must be going on if it seems too noisy.
Any SUT 10x - 20x should work fine with MM mode, but as noted the Cary's MM input impedance is unusual - but in general, don't get too hung up on loading numbers with SUTs (unless you have an egregiously bad mismatch); small loading differences from a SUT are not as sonically tweaky as for active stages.
Personally I'd try a SUT 15x or 16x. But since you say the MC mode sound is not good, I'd be suspect of the Cary altogether and maybe consider replacing it at once with a SUT and new MM stage.
Any SUT 10x - 20x should work fine with MM mode, but as noted the Cary's MM input impedance is unusual - but in general, don't get too hung up on loading numbers with SUTs (unless you have an egregiously bad mismatch); small loading differences from a SUT are not as sonically tweaky as for active stages.
Personally I'd try a SUT 15x or 16x. But since you say the MC mode sound is not good, I'd be suspect of the Cary altogether and maybe consider replacing it at once with a SUT and new MM stage.