The positive side of this problem is the stump's pretty much already pulled! Is there any advantage to cutting before trying to drop it to one side, if it can be pulled? I'd rather make it fall while standing 50 or 100 feet away cranking on a come-along or pulling with a truck/tractor than sawing and sweating inches away from the thing, and having it drive itself a foot into the soft ground and re-wedge itself 6 feet down the standing tree from where it was before. That's my experience with cutting the base of leaners that are that far over. I was thinking about flinging a rope over it as high as could be done, and pulling sideways. Pulling straight back from the stump would be very good, because it would get the top off the bigger tree, but I wondered about the stump still being rooted in the ground.
It looks to me like it is on the "back" side of the large tree it is hung in, and the two smaller ones are facing kind of to the right and forward in the picture. If most of the big leaner is on the back side, I'd get a rope up as close to where it touches the small ones and pull toward the house in the background. Looks like there's lots of trees to anchor a come-along (cable puller) to, and plenty of trees to hide behind. I'll bet you're not going to have to put more pull than the rating of a medium sized cable puller (4000 lb) on that trunk and it will slide off the big one, down the backs of the smaller ones, and whump that dish you forgot to remove into little pieces.
This is a good opportunity to get a nice heavy piece of rope added to the tool collection. If you can have someone teach you how to splice a loop in each end, that would be a nice. Other wise put a bowline on each end and toss the loop over the tree, passing the other end through and snugging it up to the trunk. It's easier to leave a permanent loop in one end (or both), than to try to pick out a knot that you have just spent time tightening with a winch! Make the loop large enough to put two fists through.
Again, if either of you are really uncomfortable with this, there's no shame in calling a tree service. Not too many people will marvel at your bravery while attending your funeral. /forums/images/graemlins/grin.gif