Hi there!
Golden week (April 29th - May 5th) in Japan is a pretty special time - almost the entire country seems to go on holiday for a week! There's a definite charm in being involved in such a national event, but it can also make travel a little tricky. Here are some key tips to remember when choosing to travel with a Japan Rail Pass during Golden Week:
Try to reserve your seats as soon as you get to Japan.
The Japan Rail Pass can be activated as soon as you land in Japan at the airport. On activation, you can specify an exact starting date up to 1 month in the future so you don't have to begin your travel period validity immediately on activation. On activation try to place a reservation for all the trips you think you will make during your holiday. If you ask nicely, and have the trains and routes on a simple printed itinerary, the JR clerk will do their best to reserve seats for you on all the trains you need. If they cannot do this they should be able to suggest an alternative.
If you don't mind standing or trying your luck, try non-reserved
It's a strange feature of Shinkansen that often the most busy cars are the reserved seating and the non-reserved cars less crowded - you can use this to your advantage if you are caught without a reserved seat. If all else fails, try using non-reserved seating with a JR Pass.
Don't travel during busy times
The JR network will be busy during Golden Week, especially at the start and end, and during morning and evening periods. If you can stagger your trip so you miss these especially busy times, you will have a much better travel experience.
I have travelled during Golden Week in the past on JR, and while it was busy didn't have any major problems provided I made sure I reserved well in advance and was flexible where I sat. In your case you'll hit Golden week for the last week of your trip so you do have some time to reserve your seats when you arrive in Japan. Also, as you will be travelling on the main Tokaido Shinkansen line there will be a full and regular service for you to use.
Hope this helps!