Wire to rope splice, advice required.....

[Brion Toss]

Hello,
This is a classic problem, rooted in expansion of the wire's surface yarns, which causes them to shorten relative to the core. There are two basic ways to minimize this effect: to get the wire as close to half the rope diameter as possible (with the wire diameter being about half the rope diameter); and by cutting the core, at the start, back to near the beginning of the splice.
It sounds like you are presented with relative sizes that have too-fat rope. What this translates to is too-strong rope, so consider beginning the cover and core tapers before tucking. You'll need to whip down the loose cover yarns when you are done.
Other details are in the "Apprentice". Do you have a copy?
Fair leads,
Brion Toss