Unfortunately, I think a mecate on anything besides a bosal or snaffle is a fashion faux paux. I have heard that when going to a bit like you are speaking of, the correct reins to use would be the rein chains attached to the bit, then the rawhide braided romal reins attached to that. Obviously you can do what you want or what makes you happy, but in traditional circles, this is the way they do it.
But if you want to attach a mecate to the bit you currently use, I wonder if you can attach a larger ring to the point where the shank attaches to the reins, then attach the slobber straps to that. Not too sure what kind of ring you could split but a larger brass one, cut with a hacksaw then braised back together might work.
Life is like a bronc ride. You gotta hang on, ride it out, and Let er buck!!!!!