Very bad idea to shift to 6 decimal places.
From a mathematical point of view it makes no difference.

But from a press point of view it will make it look like there is hyper inflation, not good.
You do not want the average person to start comparing the bitcoin to the zimbawen dollar.

It is much better to use the proper term, microbitcoin 1/1000000 or milibitcoin, for 1/1000 if the value of the bitcoin goes up, or simply just use decimals, after all most transactions are online.
 
Bitcoin it is a currency anti inflation, and it is best to reflect that fact.