It's striking that you're willing to go to these lengths on a blood trail, and do zero functional testing of your arrow system prior to hunting. Not that you should have, or are expected to, it's just a strange juxtaposition...
An elk wouldn't survive, or be able to go up a mountain anyway, after losing more than a gallon of blood. Much less gallons. Not picking nits, just clarifying some things for people reading who might think otherwise. For what it's worth - I can't see a scenario you do enough damage to the cardiovascular system of an elk to cause the loss of more than half a gallon of external blood loss, and it not be dead at the end of whatever blood trail you find.
Specific to a superficial wound (muscle hit only) - it could take several to many minutes to get that much blood out - it's likely clotting before letting that much blood onto the ground. Very unlikely scenario unless this animal is pushed constantly from the shot until recovery. You didn't do that.
Regarding any wound involving the chest cavity, specifically a one lung type shot, getting a gallon of blood onto the ground, means a chest cavity full of blood and severe loss of blood pressure/oxygen to brain= Dead elk. This doesn't mean a one lung hit is a definite dead on arrival animal. It means that a one lung hit with a gallon of blood on the ground he's definitely dead - you severed major plumbing in addition to that lung puncture. I've experienced a handful of one lung deer shots. The ones that bled like crazy were recovered because major plumbing was cut. The ones that didn't bleed literally just poked a hole in a lung. Those deer bedded, bled to death internally/drowned/couldn't get enough oxygen to the brain from a single functioning lung.
Elk are tough critters. But brains need oxygen. Blood gets oxygen from functioning lungs. Blood requires pressure to deliver that oxygen up to the brain. Any wound that results in such severe loss of blood as you've mentioned, would be really unlikely to not kill the animal who suffered it.