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.