You don't need that many anyway. Even if we assume the Academy deck has all artifacts it has in play (19 is the flashback gauntlet list, so let's use that), all cards in hand, and it somehow did this without playing no other card save 1 Academy and 1 MoM. It needs to reset with Time Spiral for the max. It has 49 cards in hand.

1) Discard 48 cards to make 912 blue mana. Play the last card, Time Spiral for effective +13 U (since it untaps Academy). 925.
2) Discard 47 cards to make 893 blue mana. Play Time Spiral. 1831.
3) Discard 46 cards to make 874 blue mana. Play TIme Spiral. 2718. 4) Discard 45 cards to make 855 blue mana. Play the last Time Spiral. 3586.
5) Discard a further 43 cards and keep the last Stroke. This makes a further 827 mana. So the total mana floating now is 4413 mana. Thus, that deck can maximum Stroke for X=4410.

That is the absolute insanity example. Realistically, they can't do that, and no way they get that many cards into hand before spending the Time Spirals. 1-2k probably suffice.