I have a different opinion, having worked in a few cemetaries:
You need to assess whether your crane can get close enough. Cemetaries are notorious for being difficult to get through with a big truck, and the expense of messing up somebodies headstone will totally blow any profits you might have been counting on.
Even navigating through the grass can leave you with a turf repair that will exceed the wood value of the tree. Be careful, people get touchy about messing with their buried relatives. You'll be trimming the trees in that cemetary for free for the next five years if you crush some irreplacable headstone.
It might be a better idea to abandon the wood value, lower chunks that you can control into a wheel barrow or log dolly, then roll it out of the area.
Cranes are rated in pounds of torque. All you need to do is scientifically guess the heaviest chunk you will need to lift, then measure the distance to the center of where the crane would be. Multiply the two, and see how close that comes to the actual rating of the crane. If it's very close, you had better get a bigger crane or cut the logs smaller.
Regarding cutting off logs and lifting them till they snap: Bad idea, in my very limited experience. Rig the log for lifting, make your cut flat enough that the log does not go anywhere. Set a plastic wedge under the log or ream the cut so that the log does not settle on your saw. Leave a nip cut on one side, then wedge it up on the side you are finishing and cut it off. No saw trapped, no sudden movements of multi-ton logs. Back away from the cut, then hand signal the crane to lift the log away.
[While he is lowering that log, take the extra strap you prudently brought with you up the tre and get it ready for the next lift. Cranes cost a bunch of money, better keep him busy!]
This does two things: it gives the climber greater safety, because he can move away from the log and be in control of his saw when the log is lifted. Sometimes those logs jump around when they are lifted off. It also reduces the probability of overloading the crane while breaking off a remnant of unknown strength. Most modern cranes come with on-board scales to evaluate the load as they begin the pick. Not much help if you still have it attached to the tree.
This is just a couple of thoughts. I haven't done a whole lot of crane jobs, and I will defer to the opinions of someone who knows better. I do know that I cut one log off, and the crane operator partly sqwooshed a small white pine because he thought the log I gave him was too heavy. (no scale in the truck)