It's possible that your new cart is not fully broken in. Phono carts change a lot with break in. More than any other component.
Otherwise, it sounds like you have a bit too much gain. MM is the lowest amount of gain, so you can't do much about it from that end. I believe the H on the ZYX stands for high output. If that's true, plugging you TT directly into your MM input should fix the problem. You won't be doing anything wrong or dangerous to your equipment. MM is the correct setting for a high output MC.
Otherwise, it sounds like you have a bit too much gain. MM is the lowest amount of gain, so you can't do much about it from that end. I believe the H on the ZYX stands for high output. If that's true, plugging you TT directly into your MM input should fix the problem. You won't be doing anything wrong or dangerous to your equipment. MM is the correct setting for a high output MC.