Can you use the shrine to get to the Master Chamber? If so, and you take the elevator up to the throne room, head to the double doors at the far end and right click, does that bring up the battle tower menu to go to the platforms?
What were you doing in the save you reverted to? It is possible you were in the middle of something where the dragon stone was disabled, and it never got re-enabled properly, or there was just some kind of glitch saving / loading.
You can try emailing support@larian.com, with a description of the problem. Maybe with your latest save they can reset the dragon stone status. As I post this it is about 7am Saturday moring in Belgium, though, so if you want to continue playing, you should delay sending in a save, since it wouldn't get looked at until Monday morning there, at the earliest.
As a workaround, if you only want to visit the platforms infrequently, you can do so in the Developer's Cut version of the game. If you start the Developer Mode version and open the 'Cheat Menu' window (F11), there is a 'goto Region' button
Scroll down the list a bit you can find entries for the locations below (full text not shown in drop down list; the part shown is bold):
001_BattleTower_Beach BTB_Laiken_Abandoned_Study_Cave
001_BattleTower_Beach BTB_Laiken_Elevator_cave . . . (initial entrance)
001_BattleTower_Beach BTI_Interior_BattleTower . . . . (alchemy platform)
001_BattleTower_Beach BTI_Interior_TrophyRoom . . . . (throne room)
Once you teleport to the alchemy platform or throne room, you can use the 'goto' button to teleport to other platforms.
alchemy: x = 55 , y = -65 , z = 230
workshop: x = 0 , y = -90 , z = 330
necromancy: x = 0 , y = 110 , z = 285
throne room: x = -25 , y = 0 , z = 2
skill trainer: x = -65 , y = -10 , z = 400
