Shinkansen - 3 Hour Journey. + 15 early arrival + journey time from wherever you stay.
Airplane- Depend on where you stay, the nearer to Handea Airport, the faster with airport limousine.
Take JAL explorer flight for foreigner which is WAY cheaper (15,120 yen (without tax), $190sgd+(with tax) 2 way)
Haneda Airport to Itami Airport. Took before not bad, 2 luggage per person too lol~ and free drink on board and it is less than 1 hour journey unless snow. but then again if snow train and plane cannot fly (I got delayed 1hr in intami due to snow last jan)
Itami Airport is just 30 min from osaka main city either by train or bus
Total Time : 30 min lumiouse bus, 2 hour early check in Airport (shopping/have breakfast after that, 30 min early be at gate), 1 hour flight, 15 min luggage pick up , 30 min journey to osaka city. Total - 4hr 15min
The JR pass is quite expensive $341 at klook, and many private train lines won't accept it, only JR will. Use the savings for the train ride and limousine bus..It is much more worth, free drinks and time at the airport to chill
http://www.sg.jal.co.jp/world/en/japan_explorer_pass/sg/