How old is your AGM battery? A while back I was having terrible starting issues with my coupe and while the battery showed full voltage it had only about 50% capacity and the voltage dropped with the first crank - not enough for a hot spark and not enough to fire injectors. I'd take the battery to someone who can load check it (I used a Batteries Plus store). If your battery is good then your idea on the coil pack is reasonable. Are you running pure gas, no Ethanol? You might think about getting a carburetor kit and rebuilding your carb(s) if the coil swap doesn't help.