Russell,
3mm wire for a main halyard is way over the top and will not like turning the top sheave, 2mm or 2.5mm (7×19) at the most for main halyards and 4mm three strand pre stretch as a tail so you can do an eye splice in the end.
3mm 7×19 is used for genoa halyards and 3mm 1×19 for shrouds, stainless of course,dont get fobbed of with galvanised.
C P 🙂