Hi Edouard,
I think I found my culprit. I was having stuttering, surging issues which I thought might be ignition related. I read that if the engine backfires through the carb, it could be a lean condition. So I thought, what would make it lean? Too much air. I checked around and I discovered that the vacuum hose that connects the transmission kickdown was old and cracked. Same for a rubber block off for a vac port. Replaced both and so far, no more issues.
I do suspect that I have starter heat soak because it is hard to crank when hot, and it not a battery issue. I have no heat shield, so I think that might be an easy fix in the meantime.
When you say you are running original wiring, do you mean the engine harness? In your photos the wiring looks very good. Though it could be just because the mechanics did a nice job with the sleeves, etc.
I am definitely a fan of 'if it ain't broke, don't fix it.' So for now you may be right, leave it alone.