Busy Shikansen over NY help

I’m in Tokyo right now and had been putting off reserving the Shikansen to Kyoto because I had read everywhere that they are easy to book last minute – when I checked the booking website last night that didn’t appear to he the case at all

I’ve got two major legs I’m planning – one is a trip down to Kyoto on the 29th and the next is from Hiroshima up to Tokyo on the 4th

I was only able to book a non reserved seat for each of these and at pretty inconvenient times – everything else was taken. Literally no assigned seats in any class on any train.

I’ve also read that people get to the Shikansen early on non reserved seats for busy holidays. How early should we arrive to make our trains? Can we get an earlier train if we get there too early? If our train is full will we get on another later train? I’m concerned that the trains will be full and we won’t be able make our trains with our luggage (one mid-sized checked bag and one carry on bag).

All of the Shikansen tips I saw seem relevant for non busy travel periods but it seems that the week I’m here is the exception and I could use some advice from people who have traveled over NY on non reserved seats which were all I could get

by LogicalPossible