I am a former Naval Officer. The UCMJ is an additional burden that polygamous people who are in the military have to deal with. It is serious business.
As with any legal question, if you are really serious the best thing to do is to retain your own lawyer, or at least do the free initial visit and get a trained legal opinion.
I personally do not know of any direct way to change the UCMJ except that it is Federal law so you can write to your congressman which likely will not do much good because there are just not enough people on this issue to get his or her attention.
I was never tried by anything under the UCMJ, but the military has a mission and my impression is they do not really want to mess with it unless you impact the mission in some way. For example, they really do not care if you commit adultery, but if it gets brought to your commanding officer's attention in some way, or you cause some sort of public shame on the military then you can be tried under article 134.
So laying low might be an option. It also helps to have a pre-arranged defense/plan of action. For example, you have to have a legal marriage to be charged for adultery. So not having one might help. I am not sure the Navy could or would do anything if you just had two "girlfriends" at home.
One warning is that article 134 is sort of a catch all. You do not have to do anything specific. They can get you for anything that is considered bad for the military. If they really want you they can get you.
How badly do you want a military career compared to how badly do you want to be a polygamist? If they found out and you got kicked out how would you feel about that? Would it be ok, or would your life be crushed?
In my experience the best lifers wanted a military career more than anything and could not imagine themselves doing anything else. They tended to fall in line and not want to stick out in any negative way. The free souls that wanted to do their own thing were not the best candidates for the military life.
On the other hand I once had a commanding officer who was gay. I mean this was never confirmed and never addresses directly, but it was well know as it was obvious. This was back in the don't ask, don't tell days (and even before). He did not have a husband (or a wife or children). Nothing could be proved. He loved the Navy, got to be a Captain and commanded a Cruiser. He kept that gay part of himself to himself and he never made an issue of it, never embarassed the Navy and did his job at a high level of competence and ended up having a great career.