The solution to halyard stretch is to pretension the halyard with the winch to more than you body weight plus live load. Then there can be zero stretch. Even with polyester halyards, I've done this many times. You should get right to the top. Really. The material of the halyard should play no part if it is pretensioned correctly.
You hands go on the mast, not the ladder. That also helps. Wear shoes that slide into the steps easily (no tread). Roll the ladder the correct way for storage and the rungs will fall open.
(The ladder is at the top of the mast. Keep your weight in and arms around the mast. Most of the steps are nicely open, as you can see, but one got squeezed by the spreader.)
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It's all in the tricks.
(Note that the ladder is only about 4 inches down. I could have done better, but this is enough. Polyester halyard.)
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