Your calculations seem a little inaccurate;
3000 (start AP) / 300 (IP change) = 10
But now the AP also regenerates each minute which leads to more AP that can be used.
60 (AP/h) * 24 (h/day) = 1440 (AP/day)
1440 / 300 = 4,8
You can change IP 4 times if you use only the regenerated AP but still you got the base on 3000 which can be used for another 10 changes.
And if you use only the regenerated AP you still got 80% of 300 which is 240 which you could use.
You can't really count on the Start AP. After all that was given so that you could do stuff when you first start the game. You can only count on the 1440 AP regen per day. Anything else is not really smart to "count on".
Seriously though with regards to IP Change. Just read the SGP forums for the currently allowed abusable features in the game.