Darren: Make sure the webbing sling is ABOVE the balance point of the mast!
Yes. Darren beat me to the post while I was busy trying to prepare a diagram, as Darren's sequence of photographs doesn't show it very clearly.
I used to operate a Hiab crane truck and over a period of time got a bit casual about making sure the loop is clearly above the centre of gravity of the mast and its rigging. One day, a mast flipped upside down, slipped out of the sling, landed on its head and flopped full length. (That only happened once! But I suppose it proves you don't want to rely too heavily on the "skill" of the operator)
I never used a loop which pulls tight at the top, finding it more convenient for the arrangement to be simple and for the loop to be not too loose, but able to slide up or down (especially at the end of the reverse operation, installing a mast). [Edit - I just realised, David has already made the same suggestion].
And anyway, if the mast is tapered I don't think a tightened loop can be relied on to carry weight. Regardless, loop tightened or not, the attachment point at the bottom should be assumed to be carrying the full weight of the mast.
(I have lifted with the loop close to, or a little below, the centre of gravity, by having a reliable person with the strength and weight to hold the base of the mast and restrain it from flipping. But that’s a bit dangerous and not recommended. I don’t like depending on the skill of other people. Better to get a high enough crane, and keep that loop sling plenty high enough if you can. You need a little safety margin too, because when the mast is out it will lean a little, and the weight of halyards or anything else hanging straight down from the mast head also wants to help the mast to flip).
Another little point to be aware of - if the mast is raked it might want to jam a little at the partners - or maybe that synthetic rubber collar which some people cast into the partners might stick (not sure about that as I never lifted a mast with that detail) - anyway, if the mast sticks a bit, the power of a hiab crane will build up tension in the arm - like a bow - and in that case when the mast finally unsticks it can jump up and out of the partners - like an arrow. (A slight exaggeration, but you get what I mean - I have seen that happen and it can give you a surprise. So much for holding the base of the mast).
As Darren says, its no big deal, and easier than you might expect. Just - be methodical and careful.