Replaced fluorescent tubes with LED tubes, the LEDs only turn on when tapped

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.

After reading Jimmy Fix-it answer I decided to give it a try to modify the Model 9000 fixture for installation of LED tubes in the Model 9000 fixture rather than throwing it away, and found the way to do it, as explained below.

The end caps are two-part plastic sections held together and mounted to the metal chassis of the fixture by plastic tabs. Besides a flat screwdriver of the proper size to work the tabs loose, you will certainly need patience and will to remove the end caps. Anyway, if the alternative given is throwing the fixture away, you don't have to be so worried that you could break something.

Photo 1 shows the two parts of the end cap of the fixture that has the input cable disassembled. It will give you an idea of where the tabs and the holes they fit into are located. Once the parts are removed you'll want to cut the wires that come out of the tube sockets as long as you can. Pull some of the red and the black wires that go to the other side of the fixture to cut them longer for easier connection. After cutting the wires you will be able to remove and discard the three parts shown removed in Photo 2.

Then strip the wires (Photo 3) and connect them as shown in Photo 4 with wire nuts.

You will connect the wires in two three-wire groups. Connect one wire from each of the two tube sockets to one of the wires of the supply line. Then connect the remaining wire of each socket to the remaining wire of the supply line.

Check continuity to ascertain that each socket has one side connected to the load line and the other side connected to neutral. It doesn't matter which side is which as long as each socket has one side connected to load and the other to neutral.

You will want to push the wire nuts into the spaces that the parts removed occupied. Then reassemble the end cap sections and mount them to the fixture. Reassembly is very easy; sections will slide and snap together in place.

With the wiring connections described above you MUST use Single Ended Power (SEP) LED tubes. Since the socket at the other end of the fixture will only hold the LED tubes in place you may cut and discard the long cables going from one end of the fixture to the other.

Hope this can help and you don't have to throw the fixture away. As you may have noted there is no cost for this modification except for the cost of the two LED tubes.