I'm not a fan of Dyna. More money than worth using my reasoning.
The stock coils have about 5 ohm for primary resistance. The stock points only draw power for 195 degrees of crank rotation. The Dyna-s draws power for 315 degrees of crank rotation. Which is 154 % longer along with a higher draw than the stock bike expected. This causes an increase in bike system load from 2.56 amps (33 watts) for the stock coils, 54% of the time (for each coil). Total ignition draw is about 35.6 watts.
Compared to the dyna 3 and dyna-s combo which draws 4.2 amps (54.6 watts) for the coil 87% of the time (each coil). Total ignition draw is about 95 watts. More than double the power draw.
The 550 has a 150 watt alternator when you spin it to 5000 RPM. Stock bikes with the standard headlight on, draws about 120 watts for the whole bike. The dyna setup adds almost 60 watts to this. You will be relying on your alternator beating the factory minimum spec to keep the battery charged. Some do, some don't. Regardless, recharging will be very slow if you are lucky.
Then, if you consider that the alternator only makes about 40-50 watts at idle, the only thing keeping your bike running is the stored energy in the battery. When that power is gone, you have a dark, lifeless bike.
The sad thing is, that unless you increase the spark gap at the plugs, or have engine mods to increase C/R, that "high performance ignition" isn't doing anything for you, except make the spark better when the battery is particularly weak. The way the ignition system works on the SOHC4, it is the spark gap that determines the actual spark voltage, regardless of what the coil is capable of developing.
You can mitigate the excessive drain by adding an inline resistor to the coils to limit their current draw. Probably better to get 5 ohm coils, though which dyna does make.
Anyway, no, your battery won't explode. It would need some stored energy to do that. Which seems low risk with an added Dyna ignition system, such as what you have now.
Cheers,
Btw, those battery voltage readings below 12.8 V shows a discharging battery.