Looking at the construction I wonder if the power cables can be improved with a fatter gauge or higher copper grade perhaps?
You're going to have to qualify what you mean by "improved" and what you believe would improve with thicker power cables (which cables are the power cables?).
Also would silver plated copper or pure silver signal cables be a bad idea?
I would strongly suggest using the wire we provide. It's actually quite expensive Teflon coated wire for the HV stuff and a carefully selected high bandwidth, heat resistant, shielded Cat5 for low level transmission. Many who substitute other wire end up with reliability problems and difficulties during the build.
Soldering interconnects directly to the internals rather than using plugs seems sensible
It's sensible until you need a longer cable, want to sell your amp, pull on the cables and accidentally rip part of the internal build apart, or move the cables enough that they break where they pass through the chassis. There are good reasons that the jacks are there.
I understand increased high frequency throughput in gain stages might cause instability.
This is not a function of the metallurgy of the wire. The Mainline is a very stable circuit. Depending on what you use, the wire you select may actually attenuate the high frequencies compared to the cable we provide.
What I would like to know is where (or if) I can change the cabling to maximise this amps capability.
Since I am investing a lot in this and building it, why not go the whole hog?
Get some fancy 10uF/250V capacitors and consider stopping there. When I have had to repair "whole hog" kits like this, it's pretty sad to have to remove all the expensive wire and random parts to put the stock stuff in to get the kit working.