Quietest time of day on Shinkansen?

Hi. Now I have my luggage (bicycle box) for my trip in spring I realise I am going to have to put it behind the last row of seats on the shinkansen. So as to cause the minimum inconvenience to other travelers what is the quietest time of day to travel? Evening travel is not an option as some journeys are up to 5 hours. Bonus question, how far in advance can I book a seat so as to ensure getting one of the last row of seats in the carriage?

Ironically, the busy time when business men travel in the morning and evening probably come with a high chance that the space behind the last row of seats is vacant because business travelers usually travel light.

But otherwise I have to confess that despite a lot of experience of traveling at different times and different days, I find it very difficult to predict how busy the trains will be. I have often been surprised by empty trains when I was expecting a busy train or (probably more often) the other way around. It depends on so many factors, some of which are impossible to account for by normal people. Not just time of the day, but also weekday, day of the year, season of the year, special events happening somewhere and on what shinkansen you will be traveling from where to where and in what direction.

Bonus question, how far in advance can I book a seat so as to ensure getting one of the last row of seats in the carriage?

One month before travel date from 10am.

Thank you Uji: My experience has been the same as yours. Trains seem to be busy or quiet at random. Also thanks for the info regarding early seat booking. I didnt realise you could book that far in advance. There are only two journeys that really concern me, Tokyo to Okayama & Maibara to Utsunomiya. I'll book early for those.

We have never considered the time of day in terms of "busyness" for Shinkansen travel (and probably won't now given the info here!!) but we have never either had issues with luggage behind the last row.
If we have needed to pile luggage up we have always gone to the luggage at each stop to make sure we don't inconvenience others underneath ours.
On one occasion we needed to leave our luggage in the space between the carriages: we told the conductor, and again, went to the luggage each stop so we didn't inconvenience others or have it put off when the train stopped!! Given that there aren't usually a whole lot of stops it wasn't an issue.
I am not overly concerned, really, about luggage on Shinkansens, so long as normal courtesy is followed. I have seen families with massive amounts of luggage all manage to courteously care for fellow travellers.
Stress less and enjoy!!

Nowadays, I always takkyubin my luggage whenever I travel between cities in Japan. It's such a reliable, cheap and convenient service. That way I won't have to drag luggage around, and also don't have to worry about causing inconvenience to other travellers.

If you take one of the "Kodama" Shinkansen, they are almost empty, at any time of the day with only few exceptions.

Fmj: Re piling up luggage. My concern is that I have one large box that will take most of the space. I will put it between carriages if necessary.
SG girl: the box is too large for most takkyubin services. Seino will take it and are an option but I am still struggling through their website and dont really want the expense.
Kyon: The Kodama may be quiet but even on a Hikari the trip is over 4 hours.