I would remove the mast. You will probably need a crane. Any marina should have one. I think the cost is something like $50 to $75 dollars around here.
Without taking the mast down, you will need a bosun's chair ($150 or so) and much more time. Each shroud will have to be removed, measured and replaced separately. You'll also want to inspect everything which will be so much easier to do on the ground. Working at the top of the mast is fine for quick jobs. Being small, I seem to get the job more than most. I enjoy going up for quick jobs but would not want to replace everything. Especially since I'll be the guy at the top of the mast. I'm guessing your mast would be about 40 feet off the deck.
Rig tension can be critical for speed. I've always adjusted my own though and nothing has fallen down yet. I just try to get the shroud tension even, by standing between them and pulling with my fingers. On most sloops, I think the mast is mostly held up by the two outer shrouds, which are anchored slightly behind the mast, and the forestay. The backstay bends the mast for sail shape and I guess the inner shrouds help support the forces on the outer shrouds. I've always started by setting my forestay and adding tension to the outer shrouds til it 'feels' right. Then I tweak the inner shrouds to be something less than the outer shrouds, even tension of course. Then I walk around the boat, look at the mast from very angle, tweak here, adjust there til I'm satisfied.
There are tension gauges that can be bought to remove the guesswork. You can get it all set up and have a local expert check the tension for you. When I say expert, I mean a fellow sailor at the marina.
Those grand fresh-water seas of ours - Erie, and Ontario, and Huron, and Superior, and Michigan, - possess an ocean-like expansiveness...They contain round archipelagoes of romantic isles...they have heard the fleet thunderings of naval victories...they know what shipwrecks are, for out of sight of land, however inland, they have drowned full many a midnight ship with all its shrieking crew. --from Moby Dick