Stabilize the mast sideways?
Ran into that issue on my ODay (Stuart) Mariner (19ft) with mast raising (25ft mast mounts on cabin top). The Mariner has swept upper and lower shrouds, and the mast is hinged to raise from the stern. Because the uppers and lowers are swept, there is nothing to keep the mast from swinging side to side as it comes out of the aft crutch. As the mast gets most of the way up, the shrouds tighten up, and the side-to-side swinging is no longer an issue.
With 2 people, the mast is manageable. One in the boat walking the mast up, and one winching. Or one to walk the mast up, and one to pin the forestay.
Single handed, a gin pole/winch arrangement is essential so that the mast can be raised slowly (or even stopped partway up) to allow checking for problems. To stop the side sway at the bottom of the lift, many different ideas have been tried, with one of the more common ones being legs that fit over the jib sheet blocks with the other end sliding up and down in the mast slot.
I went a different direction and implemented baby stays, using line with a LITTLE stretch. I added eyes about 6ft up on the mast to tie the baby stays to, and mounted a block on deck about 2" forward and 2" lower than the hinge point of the mast. Baby stays then run to the jib sheet cam cleats, although I have never had to adjust the baby stays during mast raising/lowering. With the baby stay deck point forward of the mast hinge, the baby stays also prevent the mast from sliding aft out of the tabernacle until the forestay is attached.
Work wonderfully. Tie the baby stays at the eyes on the mast, run them through the cabin top blocks back to the cam cleats. Pull them tight at the cam cleats. When I haven't used the baby stays, I've gotten in trouble with mast sway and twist, particularly when lowering. Before baby stays, more than once I dumped the mast over the stern quarter.
Fred W
Stuart Mariner #4133 Sweet P