I have to do most of your first items. But I don't have any added related structures to deal with. You're either involved as the owner or you give the yard Carte-blanche. That's expensive! Mostly because the whole process is brand new each time. Doesn't matter how many times they've pulled your rig, they have so many to deal with, help turnover.

For the best job and the least cost, you've got to be the project manager of the removal. You do as much as you can before hand-including disconnecting any rigging not required to keep the stick up, you have the necessary tools on deck(which is uncluttered). You think one step ahead of what is happening and you can make it happen quickly.

There are set charges for the mast crane at my yard but the real cost is for the crew. Figure out how to get them off your time card, and onto the next boat -asap- and your bill won't be too bad.