My take dog's not in shape; a lot of people think because they train 3-4 times a week that. Their dog is in shape, but we're just talking marks and blinds (sprints-followed by long rest periods); we're not talking endurance training, that's needed for hours upon hours, miles upon miles of upland hunting. If your gonna hunt a lot and he's 4.5 yrs. most likely you'll have 2-3 hunts with slow recovery, until the body catches up. Would help to road (I prefer a Bike) and swim him (kayak-caneo) after all you might as well get some exercise too. Using a canoe will get it done fast, with little stress on the body. I start my own dogs on a endurance regimen, ~ 1mt prior to season, and they'll still be exhausted after the first couple of hunts; but they are ready to go again the next morning and I don't see the long recovery time. My 8yr. old has a larger frame size, just got back into hunting shape after complete down time and a litter, took awhile to build her back up, but she doesn't have any of the stress symptoms your describing in your much younger dog.
Also I don't know the size of your dog, but My 10yr. old who hunted non-stop for days on end; was 24in tall, only ever weighed 86lb when he was in shape and 90lb when he was fat. He was largest framed dog I've been familiar with; your boy might do a bit better with a tad less weight, of course if your endurance training him, that will most likely happen on it's own

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The only recovery supplements I'd recommend would be to only feed in the evening and add water, to his food ~40mins after he has finished hunting for the day. This will give him longest time possible to digest, get the energy stores up for the next day and ensure he's getting enough water, as most dogs will not drink enough to replenished water stores when they are hunting. I like Glucosamine-chondroitin , but realistically your dog is too young to see much benefit from it unless he's got some sort've degenerative condition, sounds like he's just sore from over working muscles, simply because he's not conditioned for the amount of work your asking.