That math looks wrong. Calculating with 5 seconds long rounds, it would be 12(per minute)x60(per hour)x20(per day) rounds = 14 400 x 200 (Water Ring 2) = 2 880 000 / 5 280 = 545,45 miles. Or 818,18 miles with Water Ring 3.
You're right; I left out the Water Ring factor. That's what I get for doing my math in a hurry. :-P
For the Lion Army and similar numerical phenomenon, my theory is that they literally eat away the future of Rokugan: the Empire is stagnant and seemingly unable to develop in any meaningful way because every little bit of resource that should fuel its progression is poured into unreasonably numerous armies and disappears in the belly of a Lion or Crab samurai.
. . . who then die in VAST NUMBERS every time a card tournament needs to happen . . . and yet they're always able to field another enormous army by the time of the next tournament . . .
Well, this sort of strays into your magic redesign, but it's the least OP way to make them spirit summoners.
Huh? Being able to do a longer-distance version of Legacy of Kaze-no-Kami doesn't help them summon spirits.