End of May or early June should be the most suitable time, as it gets even hotter after 15th of June. Then in the rainy months of July and august there can be landslides on the way which might not be much of a problem for bikers but real nuisance for our friends on 4 wheelers.
However we would try to accommodate you as much as possible. Hoping to have you on the trip.
Had you not responded Doc sahib I would have called you myself inviting you for this trip. Apart from your company your great photography skills would be needed.