Think it through. It sounds like you are going to
motor, and you problem is to get rid of a few feet of height to get under a bridge. Your boat is a
catamaran.
A couple of lumberyard 2x4s lashed together into a crutch can be mounted to straddle the boat with the "heels" of the crutch stepped, one on each
hull near the transoms, and secured there with a lashing. Line already aboard will do the job. A third 2x4 leading forward will make the arrangement into a stable tripod. The mast will - by and by - lie in the crutch.
If the boat hasn't a tabernacle as such, you can, again with lashings, rig a tabernacle of sorts. The trick will be to do it in a manner that prevents the heel of the mast from moving away from the step while still acting as a hinge.
A sheerleg of 2 x 4s, made like crutch, must be stepped at the sheer opposite the mast step. an existing
halyard is taken to the top of the sheerleg and secured. 4-part tackles are taken to the apex of the sheerleg from each of the bows. At the beginning of the lowering procedure the sheerleg should be about 30º off the horizontal, leaning forward. As the mast is lowered aft by easing away on the tackles, the sheerleg will rise up, and the triangulation of the setup will enable you to retain control of the mast. If necessary attach guys to the mast to control any thwartships whipping about occasion by any slop where you are lying.
To raise the mast you haul on the tackles and the triangulation furnishes the vectoring you need to get the mast up off the horizontal the first few feet. After that, it's a piecacake.
There is nothing new in this. This was how replacing lower masts was handled in the sailing ships of yore if a mast crane was not available, and that was the case under most circumstances. I've adapted the procedure to suit a
catamaran, but the physics of the procedure is what it has always been. It takes lots of string and effort, but hardly any
money :-)!
I'll be happy to draw you a picture of the set-up. Unfortunately my antique Manual of Seamanship, where the procedure is illustrated and explained, is stored where I cannot get at it at the moment.
TP