amsteel shroud eye splice ?

[Kim Whitmyre]

I'm going to be making up 4 new shrouds for my boat out of amsteel grey. My mast has cleats in the traditional manner where the top of the shroud is captured. I want to put chafe protection on the eye splices (22" diameter) and was intending to use double-braid cover. But, it looks like there is no way to pass the amsteel w/cover doubled thru the amsteel: too big! Is there a way to do this, or shall I simply lace leather to the finished eye splices?

Thx,

Kim