The batt issue manifests itself on hot starts only generally. Ask them if they have checked for a sticking pressure relief valve. It may not be obvious as it sticks intermittently. If the cylinder stops on a compression stroke on the sticking side the starter can’t overcome the pressure. Hence why it’s random and not temp dependant as it has to be on the right stroke on the problem cylinder at the same time as the valve chooses to stick.
They have tested everything except the relay for starterengine but 80 km tonight and started every time, lets cross fingers :-D