Hey
Playing into the PA system with a DI should work good. Some people I know prefer it but I don't have the specifics. I don't believe you will ever be able to get close to the natural sound of your acoustic guitar playing into a electric guitar amp. Most players argue even using acoustic amps with acoustic pick -ups are not true enough to the sound of their brand of guitar. The strings are wound except for the first two E and B strings on a acoustic guitar. The electric guitar does have a special set of strings where the 3rd string is wound which is normally solid to sound more acoustic. Not to mention the string materials are different between acoustic and electric. Also you can capture the acoustic sound with microphones but you may have to experiment to prevent feedback.
Harrison