Right, using tools to remember and find out what was going on what athlete was thinking and doing, trying to do and why. What it comes to coaching, I believe most important thing for the coach is teaching how systematic skill developing and analysis can be done, so athlete will soon be able to do it on his/her own. When it comes to fine tuning these things no-one else than athlete himself can do it in the end. This is one reason why I always keep thinking it all as developing myself, that's the way the athlete will see it too.
My old school analysis tool favorite is drawing course and map on white blank paper, athlete will be able to draw the things he used for navigation and will not be able to remember/draw those he did not notice or use. And then comparing that drawing to map and those distinct features athlete should have used for navigation. Maybe head cam could be used to support this approach. Like taking a look if those distinct features he should have used were as distinct as coach thinks. If athlete sees from the video afterward how he ignores something big and very visible might get the point faster.
The place I was born and learned O has lots of low visibility terrains and I still like running such races (because others are often in deep trouble :). My constant compass use comes from there. But I don't think my technique is really that far from typical main stream thumb compass one. I never take bearing, but I always look from the map how the angle between my planned running line and north line looks like. Then while running and waiting the next distinct feature to pop up ahead I take peek at compass' needle (needle only) and see what is the angle between my running direction and needles direction. It's easy to do even in full speed in rough terrain, no need to slow down like I would have to do see something from the map. This habit gives me opportunity to use targets further away even in low visibility areas and effectively reduces risk to run in slightly wrong direction -> parallel mistake. With good visibility areas is scales down nicely, If I see the target and I have once checked the direction is right I don't have need to check the needle. You know, I don't look at the compass just to look at the compass, I have idea of the right running direction in my mind and when that feels inaccurate I peek at the needle. Also, I am getting old, my vision is pretty good but may not be for long and maps aren't easy to read these days, so the strategy is reading map well and carefully but not that often, memorize and use compass and memory to avoid slowing down in between, just some map peeks to make sure or fine tune line to next memorized target.
I can see your point, talking aloud may change things too much. But it also depends on technique. For me it wouldn't be a big deal. Talking to myself is what I already do to stay focused. I always try keeping these simple things in my mind: 1. what is the next target "marsh on left, hill with big cliff on right, I'll shoot in between", 2. direction (needle based) " slightly left from directly east", 3. tool&accuracy to hit the target "check compass but no need for extra accuracy here", 4.how far it is "~200m, almost there, will pop up very very soon" and 5. what I do when I see/reach my target "pick next target, somewhere behind the hill". To not forget what I am doing I literally repeat these simple things as words over and over again in my head. If I don't do it, I often forget what I am doing and may do something stupid, like slowing down to see is a stone on my map, loose direction, start thinking how slow and out of shape i am or something. And also if I can't repeat these things it means I don't know where I am going and so on, so that's also red alarm. So taking out loud wouldn't change things much for me. But someone who's technique isn't that simple and straight forward - uses small details he sees around, targets not that far away or reads map retrospectively - might get disturbed for having to talk aloud.
this training I planned some time ago may visualize a bit the way I try to navigate:
http://omaps.worldofo.com/index.php?id=15257
see, picking up targets, skipping over areas without even trying to read anything, counting on I will hit the target, lots of waiting time while running over empty areas (that's where talking in my head comes handy to stay focused).
I am not saying this is the best way to navigate (or good), but works pretty well for me, scales down nicely ("skipping sections"/waiting times just go away) and may be really good way to do it if ones visions is not the best or map print quality is bad and makes constant map reading difficult. So, not something anyone should copy, but maybe someone could get nice pointers for developing one's own technique to some direction.
Random thoughts - maybe better, pretty heavy stuff, makes it lighter....