Don't forget Brake Lights and Indicators as well as the rest of the continuous loads. The thing that occurs to me is whether there is an actual time limit for the specified available wattage, I don't know but from a design point of view why would Honda decide to fit a 740W Alternator if the actual design does not actually need anything remotely close to that supply?
I know that they do add a Jesus Factor with Alternators as well as everything else, I am just quite concerned with the number of very bright lights that have been added in this instance. To have 6 very bright head lights seems excessive from a current supply point of view, this effectively gives a supply requirement that is three times what was originally in the design requirement and any Design Engineer would have a minor fit if these figures were given to him to investigate!
I tend to agree with Hendo68 that we are not including the amount of current that is being supplied to recharge the battery after starting the engine...that is most certainly NOT a small amount, and if that is added to the current requirements for the lights etc. then I can reasonably assume that the required Alternator wattage is excessively high.
Add to this the fact that there would be somewhere in the order of 50A or more being drawn from the battery/Alternator (570W/12V + battery charge current) in amps and you can assume that there is a significant drop in voltage in the cable because of the resistance and heat being created in the cable itself, none of which is going to help the problem.
All this can reasonably be assumed to be the case because your Alternator did actually die!!...others, without the number of lights quoted, have not. The situation seems to prove itself, I fear.
Now I may be wrong, but I do think that the tripling of the number of headlights to 6, all powered by the original Alternator which was designed to feed only 2, and the subsequent death of that Alternator sort of explains itself!