I would cut an arm off before I'd cut a healthy Bur Oak down, especially in the cause of deer management. I've planted 200 in the past year and will do the same this year. Deer candy. You will find no acorns under a Bur Oak here in KS, just a well-worn circle path under the tree.
I'm pretty sure it was a dose of Pathways II herbicide, since I was the guy who sprayed them. They have some wild life value, but too dangerous to live around. Tractor tires are expensive, hands and feet are not replaceable.