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You state "starter engages but does not turn over" I take that to mean you hear the solonoid engage but does not turn the engine, if thats the case I would suspect there is something in the solonoid sticking when its cold and not allowing the plunger to move the full range to make the contact required to turn the starter. You may have to pull the starter and clean it up.
These are important questions. It can be mind-numbingly difficult to walk people(particularly females driving BMW cars) through these questions.
Today I disconnected the battery charger....Not knowing much about AGM batteries....
I think the biggest frustration with the starting system on this bike lies in the ECU. Truly I think the threshold upon which the ECU determines if the starting sequence is to work is set too high and needs to be lowered as I've found the battery could actually turn the engine over even when the ECU thought the opposite. Lowering the starting sequence threshold would probably save CARC bike rider plenty of money by not having to replace batteries that still have life left in them.
Wayne, end of first post said he had the direct wire starter relay fix.
The first post also states he has an AGM battery. Then later he talks about a different Shorai lithium battery.