This is one of the reasons I went with a loop of throwline on my D ring. I figured it was certainly strong enough to maneuver freely when cutting without too much anxiety. If the tree (or lead) fails, and your tie in point/lanyard combo keeps it from completely failing, you can nick it with the handsaw and be free to swing (hopefully not too violently) over to your tie in. Now if the tree fails completely and breaks the throwline, chances are it will be a bit violent but in my opinion, a decent option. Its better than being sandwiched in between two 5,500lb ropes on a failing tree (or lead).
I assume that the double fisherman's (or whatever you tie) in the throwline will decrease strength a bit as well? Probably smart to lower your tie in point a bit for some extra security as well.