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Running out of logical things to check on this.To the slightly illogical, try moving the timing first advance and then retard about 2 to 3 degrees and run it at both setting to see if you get an improvement or worsening. Have you considered re-checking the camshaft timing too?
The only input I can put into this is that as all 4 spark plugs fire at the same time, is it possible that one cylinder is over fuelling and has an exhaust valve open as the spark occurs???
It sounds very similar to the symptoms I had on a Trident 900 when the ignition pickup coil started failing. It ran perfectly until hot, then backfired and cut out. Leave for a few minutes and would start and run for a short time.I replaced the pickup coil and it was sorted. Maybe you have a rare Boyer failure? It'll be interesting to see what the testing finds.
That wiring diagram has two black wires indicated to the box, is that true? Or have they just missed thet"white" description going to the ignition supply connection? Not possible to switch those two is it?
My grammar there I think in trying to clarify, I was looking at it and wondering if it said what I was thinking So, if the two black wires from Boyer box have the same terminals? Could they be inadvertently connected the "wrong" way round? Ie earth to pos and corresponding opposite, making the Boyer box be in effect wired opposite polarity.