Based on my experience with another Kit provider based in Canada I would say that the solid core wires provided with the Kaiju kit are rather thin - Is there any special reason for doing so and would it be critical to use thicker copper / silver plated copper or solid core silver wiring?
The wire provided with the Kaiju is much, much thicker than the minimum allowable wire that could be used in the Kaiju. We provide very premium teflon coated solid core wire that will not melt by the tip of your soldering iron (though we do provide some shielded twisted pair cable as well, and some heavier gauge solid core for the filament wiring).
Are the provided wires maybe used because the wires inside the transformer and chokes are as well thin so that it just makes sense to take the same or are there any other reasons like balancing sound or even critical security reasons?
A lot of these transformers have several different thicknesses of wire depending on the winding. The choice of copper size in a transformer is quite complicated, and may not dictate the minimum required wire thickness to be connected to said winding.
How about using silver plated stranded and solid core silver wire for the Kaiju build? Where should solid core be used in general and where stranded wiring?
Stranded wiring should only be used in places where the wire is likely to move around a lot. In the Kaiju, I believe the only place we used stranded wire was for the input cabling, where we were simply opting for a higher quality shielded twisted pair cable, and it happened to be stranded.
I got two Kaiju Kits - the first one I am just about to finish using the provided wiring and parts - for the second one I am planning to use improved wiring with as much silver content as possible - does that make sense?
This is a good idea.
Regarding wire improvement and tuning possibilities: how about the PEC level adjustment pots? Any advice to replace these with something better?
There's always a more expensive pot out there somewhere. The improvements tend to be very expensive and very small.
I'm aware the the 10uF/630v polypropylene caps are a critical component for sound improvement as well - how about using Audio Note Copper Foil in oil caps or maybe VCaps here? Maybe someone would like to join me when I am going to order VCaps just to get some discount?
The 10uF caps and 0.1uF coupling caps are quite important to the sonic signature of the amplifier. Since you have two amps, I would leave one stock, then put fancy caps in the other. I am not aware of any 10uF V-cap that has an adequate voltage rating for the Kaiju, though I believe there are some Mundorfs and Clarity caps that meet the requirements.
-PB