How many of those test matches had an inform Davey Warner? He is a game winner. And sure even assuming Rogers and Doolan fail again he has got some worldclass support in Clarke, Smith, Haddin. All blokes that can smash spinners.
Davey gets his 150 and those 3 get 50 each. We can chase 350 in 4 sessions.
I'm not totally sure on the figures but I would suggest that the likes of Bradman, Lara, Ponting, Tendulkar, Miandad, Sobers, Gilchrist, Barrington, Hutton, Chappell, Zaheer, Richards, Richards, Richardson, Greenidge, Laxman, Sangakarra, Crowe, Hammond, Worrell, Weekes, Inzamanun, Hayden, Waugh, Walters, Amla, Haynes, Border, Kallis, Dravid, Or Gavaskar would have featured in a lot of those tests that didn't see a team chase over 300 in the fourth innings.
As for the 3 teams who have scored 350 or more to win in the 4th innings? I'll get back to you.