Nice job finding the Deer! But the first thing (IMO) I would have done after I saw what I believed was a (Gut-Shot) was backed off and waited for at least 3-4 hours. Unless it was getting close to dark or raining or there were Coyotes in the area.
A gut shot deer does'nt always hunch up as mentioned from the wound, but most of the time it does, and they also may act as if there not hit, they'll stand there and look around then slowly walk away untill they find a place to bed. Once bedded the animal will bed so if can cover it's backtracks and any approaching danger. The animal if not pursued will usually die within a few hours. I know this may seem mean to the animal, but if it see's or hears you comming it will run untill it cant run anymore, usually leaving no blood and your chances of finding it will be slim to none. If you leave it alone you will find it dead in it's bed. If you have Snow and can see where the animal went and have an idea where it may bed then you should back off and get some help to surround the area. Given this time to regroup and get help will give the animal time to succomb to it's wounds, and once you locate it, it will usually stand up as it hears you comming, or get up and run off slow wich should give one of the locaters a shot at it.
If no shots present themselves then the animal will usually only run a short distance befor bedding again.
I did'nt mean to get away from your topic on this but I figured if I mentioned this it would help those that have never shot and tracked a gut shot deer, and help them find it.
Remember if possible back off and give the animal time to bed, watch the direction it went and get help. If you go right after it you probably will never find it. There's no worse feeling then losing a deer when you could have prevented it.
Im glad you found the deer and you had a good shot that put it down fast, but a solid gut shot only will be a chore to find.
(BP)