How to best run long distance low voltage electric
14 AWG has 2.525 ohms per 1000 foot so clearly, at 2A, this is not going to work because the volt drop at 2000 foot is twice this and then twice again because 2 wires need to be used for send and return.

You need to push 24 watts to the far end so maybe consider a boost converter. It will step up the dc voltage at the sending end and then, at the receiving end a buck converter can restore it back to 12 volts.

I'm also thinking that to get 24 watts at the far end, it's not unreasonable to push 30 watts into the cable at the sending-end - this means a loss of  6 watts in the cable.

Given 2000 ft of 14 awg cable (doubled) has a resistance of 10.1 ohms, you could argue that to dissipate 6 watts, the current should be: -

Power = I\$^2\$ R therefore I = \$\sqrt{P/ R}\$ = 0.77 amps

Given that you need to feed in 30 watts, the boosted voltage at the sending-end will be: -

30/0.77 = 38.9 volts.

This seems perfectly doable using a booster to raise the DC voltage to maybe 45 volts (gives a little bit of extra power for inefficiencies in the switchers).

I'd use a booster because it's fairly simple, can easily have current limiting to protect the cable and uses a safe voltage range. You could repeat the calcs for 24 AWG wire using the above method to determine sending voltages for other gauges. If you are in EU, a good safe DC voltage limit is 60 volts - this is known as SELV (safety extra low voltage) - paying a little bit more than lip-service to safety specs could save you a law suit!!

Gut feeling is that 24 AWG might need more than 60V.