I have shot more moose in my lifetime than I probably deserve. But they taste so good!

They are not a particularly hard animal to kill.
A
well-placed shot with a decent bullet in the heart-lung area gets them every time.
As blargon stated in his post, quite often they show no signs of a hit, but will just wait around for a few seconds and then keel over.
I'll bet any one of those shots with the 300 would have been sufficient, but in adhering to the policy of shooting till he is down.....
However, they can go a long way if the hit is above the vital area and still misses the spine. Some even survive this shot. [ask me how I know this, lol]
A hit in the neural "spikes" that stick up from the spinal column will drop them in their tracks, but will not usually keep them down long.
A Gut-shot moose can go a long, long way, once he gets adrenaline flowing.
Likewise a moose with three legs can cover a lot of ground.
But, generally speaking, a wounded moose will not go far
if he is left alone, and not chased. 30 minutes minimum wait, an hour is better.
Once he lays down he will stiffen up [or possibly die], but in any case there is usually opportunity for another shot to dispatch him when he stands up.
I have not yet lost a moose I have shot [touch wood!].
But I have been involved in follow-up on a goodly number of wounded ones, 3 of which were not recovered.
FWIW, 4 of the recovered ones were shot in the head, and all these were still alive when found some hours later. 3 of the 4 had the lower jaw shot and broken.

Lot of suffering if these had not been found and dispatched. [How can you tell I do not like head shots?]
Regards, Eagleye