I have a couple of those RGB LED strips with the little remote controller myself.
14.4-15 volts isn't going to hurt the controller box, however the LED strip itself will run noticeably hotter, particularly if it is left on white at full brightness.
What I would do for this is put a simple resistor inline with the DC power lead going into the little controller box. This will drop the voltage down a couple volts to where the LED strip won't get as hot.
Assuming your strip is still full length (300 LEDs), resistors like these should work:
http://www.amazon.com/uxcell®-Wirewound-Ceramic-Cement-Resistor/dp/B008G50AAG
http://www.amazon.com/uxcell®-Tolerance-Aluminum-Wirewound-Resistors/dp/B00TX5X938
If you have a local Fry's Electronics, or one of the few Radio Shack stores that's managed to stick around in your area, you might be able to source a resistor there. Ohm value isn't exceptionally critical, anything between 0.75-1.5 ohm (and rated @ 10 watts or more) should work for this (that is unless you've cut the LED strip shorter, then you need to increase the ohms value by the same amount you've shortened the strip... for example the resistance range would become 1.5-3 ohms if you've cut the strip ~50% shorter).
As for the ferrite bead, it's supposed to reduce radio frequency interference (RFI), which indeed the controller does create a bit of buzzing noise on some of my radio receivers. If you have a CB or ham 2-way radio, it might be better to keep it inline (or put another one on the DC cord just before the controller box). The bead doesn't affect the operation of the LEDs themselves however.
in my experience, you will want to run a voltage regulator to keep the lights working long term. the lm 317 should work for your needs and is very east to set up.
https://en.wikipedia.org/wiki/LM317
That could work also, except that a 317 has a dropout voltage (minimum input-output voltage differential) of about 2.5 volts, so the LEDs would only get maybe 10 volts when the engine is off (battery voltage), significantly lowering their available brightness.