Cool. I have never done any type of layer so do you recommend tying a wire around the base of the tree a la tourniquet or carving around the tree?
Either method will work but wire round the trunk is only practical where the trunk is somewhat round. If you want to layer closer to the existing roots wire will be much harder so carving round will be more practical.
I was honestly thinking about cutting the bottom dead branch to the left, and below the 2 branches because both upper trunks look crappy.
JM are not always good at buds on older trunks and really hard chops on older trunks sometimes causes death of large roots that have been feeding those branches.
I'd reduce the trunks in a couple of stages to be safe. Chop to the lowest side shoot on both live branches first and hope that will stimulate some new buds below the fork. After those new buds are growing well you can complete the chop if you still want to. That should give the roots and sap flow time to adjust and tie into the new branch structure.
Chop the dead branch but I'd leave a short stub at this stage. There should be lots of dormant buds round the base of that branch and chopping the top may just get some of them to grow.