Line is Good
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For an E-35-3, I would suggest 3/8 with the performance characteristics of T-900 (or whatever has replaced it currently). Even better would be 5/16 with a cover to add some grip where it gets handled by humans or clutch stoppers. This opinion is worth about you are paying for it, I should note.
Strength is not the issue, what with the 5/16 T-900 rated at 7000# (about equal to your shroud wire!)
Be sure that whatever size line you select will fit easily through the sheaves at the masthead, and that those sheaves are not chewed up from years of wire abraiding them. We turned ours on a small lathe.
Check the turning blocks at the base of the spar, as well, for appropriate sheave profile and condition. We have been on a multi-year program to replace the old axle-design Lewmars with the lower-friction Garhauer ball bearing blocks, BTW.
We replaced all of our wire running rigging with line -- this got rid of dangerous "meat hooks" and slightly increased our ballast ratio by lowering the weight aloft.
Best,
Loren in PDX
Olson 34 Fresh Air