This is a job that definitely requires a proper lift/crane/jibboom. Fortunately you're deck stepped, I think, so you won't need to lift it more than a few inches in order to drop it.
There's plenty of trucking and moving companies that will have a flatdeck truck with a hydraulic crane that should be able to do the job at a reasonable rate. The only problem might be having an operator unfamiliar with the task.
Do you need to do this on the water, or are you hauled out? Hauled out needs a higher reach, on the water requires decent access and support alongside.
When you do this, sling the mast in such a way as to make it slightly butt heavy. Slacken all your rigging
and then take up a little tension with the hoist while you disconnect the rigging
at the deck. Gather the rigging
(standing and running) and tie it around the base of the mast. Don't forget to disconnect any wiring that may be hidden belowdecks or in the base.
Then gently lift the mast off the boat.. and guide the mast to a nearby area clear to lay it out flat. If you rig
it just right it will be easy to control as you gently lay it on some sawhorses, or a mast cradle etc.
If you have any masthead fittings like a windex or windvane/instruments it's real easy to damage those so think about that when you decide how you're going to sling and support the mast during the lift.