I turned my Micklem into a double bridle, but I do not show so it probably is not “legal”.
Many years ago I removed the chin strap since the horses I ride “told” me they did not like it, so I have nothing interfering with the curb chain.
I just got myself a bradoon hangar, I have it going on the outside of the crown piece in the center, through the brow band loops and under the elastic at the top of the crown piece. I attach the curb bit to the bridle with the bit straps and use the bradoon strap for the bradoon.
The horse I ride in the double bridle right now is a horse who is always, always, always ready to “cuss his rider out” if he is displeased with something. So far he likes my double bridle setup just fine.