I too am victim of Lyme Dz and I’m confidant the problem is not deer but the whitefooted mouse. The ticks feed, in part, off the mice. The ticks are being transported by birds every spring. Michigan did some extensive studies in the mid 80s and never found a “deer tick” on a deer. Deer tick being defined as “Ixodes scapularus” or damini They found lots of others though.
A tick isn’t going to leave a nice warm deer for a human. Ticks move from weeds to animals not so much from live animal to live animal, as fleas will do. If the deer is killed, then yes, as the carcass cools, the ticks will back out of the skin and move from the dead animal to the first warm body that comes along, usually the hunter or the meatcutter.