LED-strips, resistance, and voltage drop -- full on layman question
Some of this is speculation based on incomplete information ...
Yes, it is possible that overvoltage is your problem. The specification for the LED strips may give the acceptable range.
A series resistor will only work if the load is constant. If LED banks switch independently, or are dimmable, then the load won't be constant.
An LDO regulator is a good solution.
A simpler solution would be a few diodes in series. Probably 3 silicon diodes. I once used a diode to drop a 6V battery voltage down to supply TTL (5V).
You may also have voltage spikes on your 14.4V, put some caps after the diodes.