You mean "high" minimums, but even so, I looked at that approach (ILS 24 at Birmingham), and you have two large obstructions 800 feet below you, one of them almost directly underneath. If you get lost on the missed, there are 2000 foot obstructions you can't see. I think you're fooling yourself. You're a new instrument pilot and you don't know what kind of trouble you can get in yet.
You're betting your life on that autopilot by not watching it carefully. It can and has killed people doing that. Let a passenger take the photos, and treat that autopilot like it's trying to kill you. Because it is. Hopefully you'll find your first glitch in VMC at 5000 AGL like I did. If you're not so lucky and it happens at 800 above obstructions in the clouds, we'll be reading about your crash wondering what happened.
The issue is that your "comfort" zone is a bit larger than it should be. It's complacency. What would you do if your autopilot suddenly wound the trim all the way nose down at that particular instant? Looking out the left window, you would also get disoriented during your "WTF" moment as you swung your head to the PFD to see what the hell it was doing.