If you are on a tight deadline, its best that you take the Shinkansen.
Traveling between prefectures is the one that will take most of the time.
This Seishun 18 Kippu usually applies to those who are strong enough to travel long distance, using the slow JR train.
I've checked from Hyperdia, the difference in length of time for Tokyo <--> Kyoto traveling are:
Shinkansen: 2 hours ++
JR Rail: 13 hours ++

However, I'm not saying its not possible.
If you know yourself that you can persevere, then this is what I advise:
See?
It's a rough plan, but yeah, it's do-able.
BUT!
Assuming that you might not be fluent in Japanese language, how sure are you that you can find your way through the puzzle train lines from Tokyo - Kyoto - Tokyo?
Of course, I think the train stations would have English spelling names, but still, even I might find it hard (because my sense of directions are also bad lol).
So this is why I would suggest either take the expensive Shinkansen.
Or maybe just the cheap bus.
Buses are cheaper than the Seishun 18 Kippu (around 4000 Yen++ per destination) but it travels as slow as the JR Rails (or maybe slightly faster... just slightly).
Using JR Rail, at those time of night travel, you might have to switch trains, which means more added confusion of trying to figure out where you are at that time LOL

At least with bus, you KNOW you are going to reach your destination directly non-stop (they'll stop occasionally for their customers to buy food or go toilet).
However, I dare not say more on bus because I've never taken a bus to travel long distance.
The furthest bus ride I went was from Shibuya to Mt. Fuji, but that was on a tour group.
actually night trains , im assuming moonlight nagara from tokyo-nagoya doesnt require to change trains. personally i prefer buses. if u book early ,its even cheaper.
Emm..Japan domestic Flight also cheap...Most Japan people like travel by plane rather than Shinkansen. Can you see the domestik flight from tokyo to osaka , kyoto , kansai , chitose all by flight more. Japan is the only in world domestik flight need using B747 and B777 to fly domestik...too much passenger
i agree. when i flew from osaka/itami to chitose, i was so shocked to be sitting on a 777