Micing this guitar is going to be challenging because it doesn't have a typical acoustic guitar sound because of the lack of a thicker body and no sound hole. You will get lots of string sound, but not much 'body' sound.

It sounds like you are not happy with the acoustic sound from the A6 pickup system. I would first start saving for an acoustic guitar that sounds more like an acoustic. Godin's acoustic guitar brands are generally great values and since it's a Canadian company, might save you some loonies, instead of trying to find the magic solution to 'un-piezo-fying' the output of the inbuilt pickups.

Try the Craig Anderton EQ tip above, but if what you are really shooting for is a more natural acoustic tone, it's going to be less expensive getting a more proper acoustic guitar, than it is to find some kind of signal processing to get a natural tone out of the pickups.

As pointed out by Mario, you can get a very inexpensive large diaphragm condenser mic to go along with the guitar later on.