Well, I'm not an insurance or healthcare expert but...

I would divorce state ID, which is a gender identity from biological sex on medical forms. It's not like they ask you to drop your pants to prove you are male or female when you get your driver's license. You just state your gender.

The AMA could start pressuring doctors via suspension or revoking of their license for denial of care of transgender individuals.

Better education of gender issues in medical school.

Civil lawsuits against insurance companies for denial of coverage.

Starting a transgender cooperative insurance company to either fill the void or set a new standard. There's a real business opportunity there for someone bold enough to pursue it. If you started one that wasn't exclusively for trans issues but did not disqualify them that was competitive on the market, you might be surprised to find you're not as alone as you think. Women are being denied access to birth control. Men and women are being denied optional sterilization. Others have and will be forced again.

How about identifying doctors specializing in trans care in each major city and where there is a lack, funding the education via scholarship to fill the void. You can make practice in a certain area and specialization in trans health care a stipulation of the scholarship.

Somebody somewhere makes these decisions. Infiltrate the industry to effect change from within. There's also going to be a stockholders board. If enough people who want better healthcare for trans issues and others but enough stock or convince those that have it that these issues will generate revenue, then they'll force the actual companies to change their policies.

If it costs them money or makes them money, they'll give you what you want.

You have allies. You should utilize them. Advocating for highlighting a problem is one thing. It's the first thing. After that comes research, a strategy, a plan, organizing, and action.