Hi Giga,
The best time to remove the CM is in Spring when all the new leaves are well grown. But since you have no choice, this time of the year is OK, since it is dormant at this time and like Vin and just.wing.it stated, the CM is tough. It can survive even with the big cutting!
I can see we can chop the trunk as yellow lines.
If you want to dig these, you have to be prepared for a heavy work due to big hard roots to be chopped. Just use the axe to clear one side of one tree (A) first, then use ratcheting tie down strap connect tree A to tree B, then ratchet the strap. The tree A will be pulled over, it is easy for you to use the axe or saw to cut the root down in the base. You also can use the pick up truck to assist you in pull the tree over.
If you don't want to do yourself, you can ask the owner when the tractor will do its job, then you can come over on that day to get the tree without sweat!
Some people will be glad that you take these pieces for them, otherwise they have to throw them any way. One time, I had to pay the guy $40 to do heavy work for me, but it's worth!
Good luck.
Bonhe