I have spent many years setting up for LR hunting so have no issue with the process if proper steps are taken. If you don't mind a bit of constructive criticism, consider the following through the eyes of a competition LR shooter and ex LR hunter.
Range, and ambient weather understood. Let's call it 800yds for easy math.
Wind - obviously not strong and with visible cues - water, vegetation, likely wind meter of some sort.
Time - animal is not stressed and moving slowly given the time it took to go from where you first saw to where you took the shot. Time to set up the shooting position.
So assuming all the above is correct, the first shot (cold bore) lands about 3.5ft above desired point of impact (guessing on size of moose). That is approx. 5 1/4 mins high.
Second shot is maybe 3 feet low given that you hit the water on the standing moose in 3ft of water. Approx 4.5mins low.
3rd shot connects enough to stop the moose.
Typical drop between 700 and 800yds with a 210gr VLD and 300WM is likely around 2.5 mins. Just run the numbers for your load.
Usually, that first shot is my best as I have time to set up, get all my ducks in a row and concentrate on a clean break. The shot ends up not doing what you want and given all that you have practised and planned, that doesn't make a whole lot of sense. The next part is typical and that is a bit of panic.
2nd shot is rushed/over compensated and quite easy to be pulled badly... so it goes way low. Not ideal but understandable.
Refocus happens from known info, a correction is made and the third shot connects enough to get the job done. Location unknown vs POA. Good BUT that is not the problem.
The problem is how far off that first cold bore shot was. Given the practise and load tuning that is required for this type of endeavor, I would know exactly where that first shot is going to land at all ranges I will engage. I may be out as much as 1 min given the changes in ambient conditions, range, light, excitement, whatever but that shot is going to hit in and around that 5 ring.
That 5 ring would have put that moose down, simple as that. Given the trajectory of the bullet and rd used, you could be a ways off in ranging and still connect, no worst then the 4 ring which is still plenty tight to end the event.
So this is not to critise the act but in the gear, set up and possible practise.
You may have a scope that is not tracking, a gun and ammo that is not as good as you may hope for. The need for more trigger time to ensure that first and follow up shots go exactly where you want.
Ask any F class competitor and they will tell you the same thing. Set up, know the range, dial the scope, SWAG the winds, send sighter 1... that shot is expected to land within 1min of POA for elevation if not even with the center of the V bull. Windage may be off but not a huge amount.... hopefully.
Windage is the only real thing we are trying to figure out and with a high BC set up and light air, that amount of error will not be big. For hitting a moose at LR, it better not be.
So consider, more testing, more practise and a serious check on your gears real world performance. Something is not working well for you and should be figured out.
When I was set up for LR shooting, the process was to locate the game, NOT hit the game. That part was simply range, dial up, dope, fire, go retrieve. The hard part was getting in front of the animal. The harvesting was no more demanding then a 100yd shot otherwise, that shot was not taken.
I tested by doing a bunch of field shooting on milk jug sized targets placed randomly. If I could not connect on a cold bore (and up to 2 more followed in quick succession), it put limits on both range and conditions that I would/could engage. It was a no brainer to see if what I was doing worked or not.
Hope this helps...
Jerry