This is the "immortal problem" that rugby league has. How do you pick an immortal out of Smith, Thurston, Inglis, Cronk and Slater? All five of them have strong claims. The 98-03 and 03-08 periods have Tendulkar, Gilchrist, McGrath, Warne, Ponting, Hayden, Kallis and Steyn all in the running.
Then you have dull periods like 88-93 where the Windies were transitioning from the Marshall years to the Ambrose years, Warne wasn't on the scene yet and though the Windies were ahead of all during that time, none cam really lady claim to being the pick of the bunch.
So here is my attempt.
88-93 Gooch
78-83 Gavaskar
03-08 Ponting
73-78 Richards (c)
13-18 Smith
63-68 Barrington
98-03 Gilchrist
93-98 Warne
83-88 Marshall
08-13 Steyn
68-73 Snow
There are two oddities to this. Gooch is the player who looks most out of place in an ATXI but he was seriously good in this 5 year period, scoring by far the most runs at an average of nearly 57.
The second is that Richards appears a bit earlier than others have him. That's ok though since he was still in the top ten run scorers during this period and did so ast an average of around 56.
I've made Richards skipper since I made Ponting number 3.
This side would push any other ATG sides sans-Bradman.
Tendulkar very unlucky to miss out but his awesomeness is mostly due to his longevity which this exercise distinctly avoids.
Barrington can roll the arm over as the fifth bowler if one is ever required. With ask attack boasting Steyn, Marshall, Warne and Snow you have an attack good enough to take 20 wickets in any conditions.