Can't transfer minor child's progress from old phone to new phone in PvZ: Heroes

Title pretty much says it all.  If your child in the US is <13 years old, the game does not give them the ability to link to the EA account (if it exists) or Facebook or anything else.  But the game also doesn't save your progress to iCloud (which would be the easy way to transfer the progress to the new phone).  Anyone know how to get the progress from the old phone to the new one in this case?  My child has used his allowance to buy premium packs and such and I absolutely refuse to throw away not only his time but that money.  I'll be on the phone with EA if no one here has an answer.

Thanks!