My guess is the coil packs aren't likely to blame. When I had the coil pack go bad on mine, it was a really violent shaking when it completely gave up the ghost. So bad you didn't want to consider driving it. Up until then, there were occasional large shakes but nothing much in between. That is to say, it either completely worked or completely didn't.
The backfire is disconcerting, though, and gives more credence to an ignition problem. Unless your spark plugs are nearly new, replacing (or at least inspecting) all of the plugs feels prudent. When were they last changed? Are they all NGK PLFR5A-11? People have had problems with other brands and even models.
I'd run through the troubleshooting steps
in the FSM for P0300, or at least as many as you can.