You could also do a rough a "no heel" approach and you see if the center of gravity can counteract your weight at the top with no heeling (benefits from hull shape) needed for righting moment.
If the center of gravity is 1 foot below the center of buoyancy, you can climb up to a height of H before you'll get any heeling:
5,400 lbs x 1 ft = 200 lbs x H ft
H = 27 feet
You could always lose a few pounds. Just sayin'.... Leave your heavy tool belt at the deck. Take you shoes off. Don't eat a big meal before hand. Shave. Skip the big belt buckle.
Saving 15 pounds looks like this:
5,400 lbs x 1 ft = 185 lbs x H ft
H = 29 ft
Just remember that you'll be suspended from a halyard at the top. So even if you go part way up, if the boat heels, you'll be dangling from the top. You have to use the full height in you calculations, even if you see your center of gravity staying a couple feet from the top or many feet from the top. (Picture this: if you don't have a loop around the mast as you climb, then when the boat heels, you'll be out over the water creating more heeling force than if you were against the mast.)
Anyway, that's my method for doing a rough calculation. Anything more and you have to look at the righting characteristics at angles of heel. (How the center of buoyancy gets farther from the center of gravity as the boat heels.)
Use a loop around the mast and climb slowly?
I'm a guy with a calculator, not a rigger. Take the above with a hefty grain of salt.