LED controller

[Dexter12353]

We are installing some of these LED tape strips.  The led strips look like this:

They run on 12 volts DC.
From china for about 5 bucks, you can get these remote controllers that can make flashing effects, fading, brightness, etc.  They adjust the brightness via PWM.
These remotes only have enough bang (limited to .5 amps) to run 20 feet of these lights.  We would like to run approximately 80 feet (4 strings, all starting at the same point, imagine + shape)
These remotes have a common positive buss, and they switch the negative.
Some screenshots of the controller/remote module:
Top w/drawing:

Top w/o drawing:

Bottom w/ drawing:

Bottom w/o drawing:

I have investigated Solid State Relays, but they are expensive.  I have some 2n3055 transistors laying around, and various resistors/capacitors, and I was wondering if I could build a circuit with the transistors to increase the maximum amperage.  I am not very experienced with building circuits, so that's why I've come here for help.

Thanks for all of your time!

[David_AVD]

You can also buy "RGB Amplifiers" very cheaply (< $10) from eBay or China direct.  The original controller feeds into the RGB amplifier and that can usually have up to 4A or 10A per channel on it's output.