I would suggest stay away from anything mercy. As they are a fairly religious hospital. So they can deny you anything that's against their religion. Now there are probably a few doctors in mercy that are cool but I don't trust it.

My trans daughter sees Dr Kate Kilgo at Cox Steeplechase and she is amazing and incredibly inclusive.

Not a fan of Burrell, personally. Ginger Holczer is a good therapist in the area that helps with trans people if you need an in person therapist. Strongly recommend Small Victories Wellness if you're alright with online support. They are a really good for online sessions.
For PCP check out Adam Bolyard.

Im openly LGBTQA+ Ive never had a good experience with mercy nor would i trust them with that kind of care you're seeking. Mercy treated me like I'm a child who doesn't know what I'm talking about. If you value your sanity DO NOT deal with Burrell. They're horrible and did a horrible number on me when i was a kid that I'm still combating to this day, mentally. Lakeland is just as bad and staff deliberately antagonize patients. The one time I went to Jordan Valley they treated me like Mercy and didnt listen to me. I ended up having walking pneumonia that later I had to seek treatment elsewhere for. However. On the psychiatric side, my sister and her kids are doing well with them. Cox has been the best experience Ive had with any sort of care Ive needed. My current therapist office is the Ozark Counciling Center, they are very LGBTQA+ friendly and while you may not need a therapist they may be able to recommend a psychiatrist that will help you.

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The clinic at APO will see patients even if they are not HIV positive. Probably going to be hard to beat their staff in terms of being trans inclusive.

Jordan Valley is very trans friendly. They even used to have a provider who prescribed hormone replacement therapy at one time.

Is that a gallon of PCP you've got there?