I didn't use the JR Pass for my trip (probably should have but it was last minute stuff) and I just used the smartEX app to book shinkansen tickets the night before. There's one literally every 5 mins (it's insane) so you'll always find one with some seats, but if you have oversized luggage you need to book the back seats to store it behind the seats (my normal-ish sized suitcase could just fit up-top on the baggage stands though). Tokyo to Osaka was about $150 each, so if you don't have the pass it's probably not worth going back. Remember you activate your pass for 7 days at a dedicated time, not just when you get it. So you can spend a week in Tokyo first, activate and then go balls to the wall for the next week.That is already cheaper
For a 7 day pass it is only $965ish and I assume it is unlimited trips in that time?
So I could theoritically leave Tokyo on day one go Nagoya for a couple of days then onto Osaka and back to Tokyo in a week?