Addressing your original question of where to transit via: in May, weather will likely not be an issue via EWR or IAD. Having never arrived at IAD on an international flight, my only experience to speak to is EWR international arrivals. Transiting from B to C landside via AirTrain is not the end of the world. If you are spending material time in the airport, with no UC membership (and even if you have one), EWR will be better. For all the hating Newark gets on this forum (and for their customer service, it is deserved) - the 'temporary' IAD terminals are terrible. Terminal C (and especially Terminal A, but you won't be flying out of there on this routing) is not that bad at all.

I would not be determining your routing based on the domestic leg - you will be jetlagged and feeling terrible regardless of where you transit for your second leg. Going via IAD on the 763 will be more pleasant in economy. The only roll of the dice is that the nearly all of the 763s are very old, so to some degree, you are playing Russian roulette on whether your flight makes it (just see the cancelled international flight thread). At end of the day, you need to prioritize what is important. If it is the layover domestically before heading to the West Coast, I would go via EWR. If it is anything else, I would go via IAD.