@IK-NWhunter ,,,,I've experienced this more than a few times over the last 40+ years of archery hunting,,,,,, it is never easy when an animal is hit and not recovered! That sick feeling will stay with you for a good long while. There will be times when everything seems to go as scripted and the outcome is not what's expected.
The "Plywood" sound was definitely a shoulder bone hit, from experience here. The cough indicated that the arrow penetrated into the chest cavity and the bull is now dead, no sugar coating it. Once the bull was bump out of his bed, well, they can travel a long ways on one lung. With that, a mortally wounded bull will usually pick the easiest route available after being jumped from it's bed. Knowing that, a hunter can eliminate a portion of the surrounding terrain and adjust the search area accordingly. Here is where experience plays a huge part in the recovering of the animal. As you stated, a hunter can be proficient with the bow but experience dictates the reaction and outcome once "THE MOMENT" arrives.
You are correct about the arrow plugging the hole and not providing a good blood trail. I think that it is a combination of the dense shoulder muscles, the bone itself and the arrow that greatly reduces the blood to exit and fall to the ground. I have never had a bull go over a few hundred yards if the arrow makes it into the chest cavity. They will usually bed once they realize that they are in trouble but the chest cavity will have to fill up before they expire. It may take some time for the chest cavity to fill before the bull starts to cough up blood while bedded. Also, the bull will usually bed down on his good shoulder,,,leaving the arrow side high and dry. The blood that does seep out of the wound will be soaked up by the surrounding hair and may not make it onto the ground. Once the chest cavity fills, there will be blood coughed up...and usually a lot of it.
I have lost one bull that was hit in the shoulder and it played out very similar to yours. The sickly feeling sucks bad but at least I learned not to rush things,,,,,extra time is needed.
Searching through my photos, here are a few examples:
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The above bull was hard quartered to at about 10yds. Hugged the shoulder a bit to close and heard the "plywood" crack when the arrow hit. The arrow chipped off of the should bone and berried to the fletching. The bull whirled at the shot and ran 30-40yds, stood for a moment and then walked off down hill. There were only a few small drops of blood in the snow where the bull stopped and no blood could be seen from that position along his tracks. I backed off, built a fire, and waited about four hours before returning to the bulls tracks. With the snow, tracking the bull was very easy, but, in the first 150yds I only viewed two dime sized blood spots. The bull walked straight down hill until he hit a bench. He then turned and followed the bench 50-60yds before he bedded. At that spot, the bull had three separate beds. The first bed had one little pink spot of blood in the snow. 10yds away, the second bed had quite a bit of blood. Once the chest cavity filled up is when the bull started to cough up blood. The bull didn't actually bed the third time but tipped over and died about 20yds from the second bed. The bull bedded 200-250yds from where he was hit. Almost five hours later he was still warm and hadn't started to stiffen up yet. With that, he had expired not long before I found him. Without the snow, and with almost zero blood, this bull would have been hard to find. With that said, I knew that a wounded bull would find the easiest route and the below bench would have been the place to look for him. This bull would of been lost if pushed out of his bed and ran down hill below the snow line. Note that I placed a green circle around the arrow hole that the arrow was pulled from.
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This bull, 10-12yd shot, standing broadside. The shot was very steep down hill, think tree stand, "plywood" crack at the hit. Bull lunges 5yds and then just stands there, sound familiar? Movement of trying to load another arrow causes the bull to bolt straight down hill into a downfall maze. I could hear the bull's progression through the downfall and knew that he had angled up canyon. I found the back third of the arrow between the hit location and where he stopped as it was snapped off when he brushed a tree. Again, only a few small drops of blood was found where the bull had stopped. Backed off and waited hours then returned to try and track the bull. The steep downfall slope only gave up several slight smears of blood where the bull had jumped over high fallen logs. That lasted approx 70-80yds and then dumped out on a bench above a line of cliffs. At that point, I found one spec of blood on a light colored rock. A hundred or so yards up the bench and I found the bull. This arrow went straight through the blade and through the off side lung. As the picture shows, there was very little blood coming out of the arrow hole making tracking damn tough. This picture does show the large pool of blood that the bull coughed up once the chest cavity filled up. This bull had started to cool down and stiffen up when found. So he didn't last as long as the above bull in the snow....but....and again, the bull would have been damn near impossible to find if jumped out of his bed. Time and patience is always an archers friend, try not to push the situation.
It really sucks to loose any animal and I commend you for notching your tag. With that, I once shot a bull in Oregon that had two different style broadheads along with two different calibers of rifle slugs encapsulated throughout his body and he was 100% fine,,,,so not all hits are fatal!
I sure hope that this helps at least one hunter in the next few weeks. Good Luck to all and shoot straight!