(The new plan - thanks to Dheeraj, RK and ANup Sir and many more guys from bcmtouring.com)
June 4th - Day 1 - Bangalore -> Virar (NH4 to Mumbai and NH8 to Virar - 1027 Kms - estimated time 14-15 hrs rotated between 2 drivers )
June 5th - Day 2 - Virar->Jaipur-> (NH8 - 1108 Kms - 15 Hrs)
June 6th - Day 3 - Jaipur->Kud/Patnitop (it will be tough drive) by pass Jammu at Chak Dayala or Samba, will save you around 1 hour
June 7th - Day 4 - Kud/Patnitop - Srinagar, Stay near Dal Lake, on Bulevourd Road, good location, and that is the road you will take for the onward journey, and it comparativeky safe too. Also you will reach Dal by 1:00 Pm if you start early around 5:00 Am, so you can think of going upto Sonmarg. That will put you in very good position for next day. And its much more safer. So choose between view of Dal or view of Sonmarg. I would go for Sonmarg :P
June 8th - Day 5 - Sonmarg - kargil, even try to reach Sanko if PWD GH is functional there, Kargil is dumping ground of Kashmir, sadly pretty messed up place, Kargil have a MASS, if required and Petrol pump
June 9th - Day 6 - Kargil - Rangdum relaxed drive
June 10th - Day 7 - Rangdum - Padum relaxed drive
June 11th - Day 8 - Padum - Lamayuru relaxed drive
June 12th - Day 9 - Lamayuru to Leh
June 13th - Day 10 - Move around Leh Palace/Shanti Stupa/Thiksey/Shey/Hemis/Hall of Fame and Permits
June 14th - Day 11 - Leh - Khardungla - Leh, if you start early, you can come back by 3-4 Pm. And if required get the car checked at Druk MASS,
June 15th - Day 12 - Leh -> Pongong Lake -> Tangste, stay at Tanste, you will not have to rush back to Leh and can spend more time at Lake
June 16th - Day 13 - Tangste - Upshi(Petrol) - Mahe - Karzok(Tso Moriri), you will have to keep deisel in Cans as well, From Tso Morir till Tandi
June 17th - Day 14 - Tso Morri Lake -> Sarchu
June 18th - Day 15 - Sarchu Manali
June 19th - Day 16 - Manali -> Chandigarh
June 20th - Day 17 - Chandigarh -> Udaipur
June 21st - Day 18 - Udaipur -> Pune
June 22nd - Day 19 - Pune -> Bangalore
June 23rd - Day 20 - One back up day , in case of any twist