You're right, shortwave, on all counts.
I would drive around looking a bit but the place is 40 miles from home.
I've heard this rumor of deer "plugging" wounds too and stories like yours tend to add some level of believability to it but I'm left with the nagging fact that I've never seen, or known of anyone who has, a deer that tried this unsuccessfully or found a deer dead with its wounds "plugged". It's hard for me to imagine that they do it with near on 100% success of not just stopping the bleeding but surviving otherwise fatal wounds.
Least ways, I'm confident that this deer is dead. The distance it covered is small to where it crossed property lines, it did it at 100% "turbo boost" speed and, even with it running full-tilt, the blood trail was easy to follow in the dark with just headlamps.
The conundrum is that the deer that you most want to know where you hit are the same deer that you'll never know because you only want to know because you never found them.
When next I hunt, I will have home-made luminocks installed. At least then I'll know where I hit.