Unit 36 for the most part is Eagle's Nest wilderness area. I know about 1/2 of it real well. It wil be tough to hunt this area and stay at a cabin each night. The area is steep and has got awesome high country.
There's a pull off under I-70 between midturn and avon, you can park under the bridge and hike up the mountain to the south. It's a long hike to the top but there are alot of elk up there and you may be able to buy a leftover deer tag and hunt archery deer along with elk. If you stop at the rangers station in Midturn, you can access the same area by hiking up the trail behind the building.
Or head up to Grouse mountain, it's just south of the Beaver Creek ski hill. You'll have to stop at the local Ranger's station for directions.
Or if the lift for Beaver creek is still open, ride the lift to the top and drop off the back side of Beaver Creek. You will need to camp fo Grouse Mountain or the back side of beaver creek.
Or you can head to piney lake which is just north of Vail, good elk heard but there will be alot of hunters as well.
If your staying in a cabin in beaver creek, it will be hard to get into elk because you will have along way to travel everyday to get to them, car and then hiking time. you can drive to Piney lake in like just over an hour, and get hunting from the truck. But to get away from the crowds there you'll need to make some longer hikes. We used to backpack it for 2 or 3 days at a time and get into elk.
Good luck.