What leads you to believe SP has a military background? He/She doesn't walk or stand like someone with that background. (Or those I have known, anyway). I also find it hard to believe that the moon phase entered into this. It doesn't seem to me that the planners of this were that......detailed. Too complicated. What makes you say that the moon phase was a contributing factor? Not being snarky, just interested is all.
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They do walk with a military gait. What we see with the left leg that changes it up is caused by the way the shin guards are strapped on that leg - which is not how shin guards are strapped. I believe that strapping to be necessary to strap a holster for a long barrelled pistol to that lower left leg. Had SP not done that their gait would be much more like what you see with geared up military or tactical teams.
I believe we are dealing with a meticulous planner. That said, I am confounded by the idea that somehow the planning would be less complicated. We have someone who has managed to create the situation where not only was the murder not caught on camera but neither was their exit from the church. Someone that probably left no physical evidence of their identity at the church or on the victim. Someone that almost certainly left no traceable movements other than what was seen on video. My take is that if you are going to go to all those lengths to cover all of those bases there were more planning elements that aren't as apparent. I don't believe SP was winging any of this. Nor do I believe any one person could get lucky so many times to not appear on camera, not be seen entering or leaving the church area, not leave much physical evidence leading back to them, etc.
The moon phase can determine how bright at night it will be. How well can you see outside at night under a full moon when the skies are clear? What about when there is a new moon? The brighter it is the better chance you will be seen. It is something that military operations take full advantage of when timing an operation, along with the weather. The less visibility the better. For what it is worth, you can find the moon phase calendars for any day even hundreds of years in the future (or past) in about 60 seconds on a Google search including the moon rise and set times which would tell you whether the moon would be visible at night at all.
I have said before that I believe SP is very intelligent, well beyond average perhaps 90th percentile or more (that is, smarter than 90 percent of anybody in this country). I also believe them to be very disciplined. When coupled with a planning ability that makes them an especially dangerous adversary. I believe them to be smarter than any of the investigators LE has on this case. SP's mistakes will not be apparent to most investigators. They will be apparent in hindsight should they get to SP and arrest them. I believe the biggest mistake is the plan itself since it would narrow down potential suspects rather quickly.
The reality is that SP could have killed MB outside the church, or even outside her home as she left for the church, just as easily and left even less to go on. SP chose to do otherwise as I am sure those other options (among others) would have been obvious. I am of the belief that the biggest clue to the identity of SP is the level of planning that went into this. Incidentally there is no one on the search warrants that would be this intelligent nor evidence this kind of planning capability. They aren't dummies but they are smart enough to approach this level of planning. When I look at this crime I see situational awareness, risk mitigation (in spades), use of devices like disguise and misdirection, that are all complicated when executed, apparently flawlessly, as part of a comprehensive plan. Others see differently.