Can't get more than 2000 mana. Can't pay a casting cost over 999.
Halana and Alena + Bronze Cudgels is frightening. Add Cradle Clearcutter and you can reach very high numbers.
But you can't really take advantage of them. First of all, regardless of Cradle Clearcutter's power, it produces a maximum of 2,000 mana. However, even at this (comparatively) low number, paying for an X cost spell takes longer than you have. The game timer begins before you can finish tapping +5.
My suggestion is that since the game allows high numbers, it should have a GUI interface that can accommodate them.
Even Sparky timed me out.
Supposing your 62160/62172 Cradle Clearcutter could add an amount of green mana equal to its power, not even Sparky has enough patience for you to punch it in at +5 per tap. (I reached ~20,000 before the timer showed up and ran down.)
Once the number you can input is over 100 or so, the interface needs to change to accommodate it. As it stands, anything above 2,000 toughness or any player above 2,000 life is effectively immune to a fireball. The match timer runs out before you can finish paying for it.