Your use of 12 gauge to an input of an amp is severe overkill. The whole reason of having a higher gauge wire is to carry current. Since you only need to get a signal to an amp, you can use stock gauge or even less. Wont hurt anything to use the fat wire, just wikk not get any improvement whatsoever.
Btw twig, speaker wire can handle much more voltage/current than an rca cable. Look at lamp cord, commonly used for speaker wire. Have a fire extinguisher handy when you wire up a lamp with an rca type or sheilded cable!
Rca/ sheilded cable is for low level signals. The rca out that says four volts is still a low level signal. There is no current behind it, and the four volt level helps reduce picking up induced noise in cable runs. You reduce the gain in an amp and the induced noise is attenuated.
Unsafe, (like the name!) run regular cable to your crossover, and run short rca to the amp. You can use the fat wire, but it wont buy you anything.