Converting LED String Lights from Battery to DC Power Supply

As I don't know the interns of this dimmer it might switch when the alternating voltage (and therefore the current with resistive loads) crosses zero. To detect the phase (crossing 0V will occur at 0° 180° and 360° which is again 0° - you might want to look it up here: http://en.wikipedia.org/wiki/Phase_(waves) ) and the type of load (e.g. inductive loads delay the flow of current depending on their inductance and the frequency in relation to the voltage. I could not find a text on wikipedia describing that so here's a plain image: http://people.sinclair.edu/nickreeder/eet155/PageArt/phaseInductor.gif

To detect the type of load it has to observe the mains line for a short period of time without regulating it.

The issue does not occur on light loads because most dimmers can handle inductive, capacitive and resistive loads quite well on low power levels.

By letting the dimmer "cool down" you may erase its short term memory so it has to resynchronize every time you switch it on.

Again: As the internals of this dimmer (or better: the two) are not known I can't provide a better answer. A newer hardware revision usually improves the product. Also chinese manufacturers tend to produce lower quality products as seen here: http://hackaday.com/2012/08/15/buying-cheaper-electronics-and-not-saving-money/

While @cde 's comment is noteworthy, I try to answer your question as good as possible. One note: the right word for the things providing power to LED-lighting systems is "LED driver" in the US and "electronic control gear" (ECG) in the rest of the world. Naming it transformer leads to confusion. I'll use "transformer" here, for consistency, though.

Option 3 will yield the probably worst result. 112 ft will pile up astonishing 35 A current on your wires. While gauge 12 is sufficient to bear that load without causing fires, it will suffer a significant voltage drop of up to 1V at the end of all striplines. This means you may encounter dimmed or even no light output from the most remote LED striplines.

Option 1 suffers the same drawback but not to this extent.

Option 2 is probably the best option for minimized power loss and homogeneus light output.

You do not write if all your 8ft tubes are adjacient, so there may be significant cable length to add for the calculation of a voltage drop.

I'll try to summarize some general advice for your situation.

1. If you can, mount the transformers as close as possible to the LED strips in a 12V system.

2. Compare prices. Single huge transformers do not necessary save much money compared to smaller ones. Smaller transformers can be placed closer to the LED and in confined spaces.

3. If you have to run long lines with high light output, switch to 24V-Systems. Transformers are smaller, you can chain more LED-strips together and you can use longer and thinner cables to connect your LED-strips.

4. Pay close attention to the specifications of LED-strips and transformers. In most cases a 12V transformer for halogen lights is incompatible with LED-strips. You need a LED driver or ECG (electronic control gear) specifically designed for LED lighting.

5. consider using retrofits, as cde suggested. But you have to pay close attention if they meet all regulatory laws in your country. There are plenty retrofits on the market which pose a fire hazard or hazard of electric shock to their users.