For 45 feet, I'd consider #12 wire. For that distance, assuming 7.5A of load, you'll already drop more than a volt. That doesn't consider the additional voltage drops for distribution after you wire to the tracks.
The AIU shouldn't be a problem if you use heavier wire for the power. The issue with the distance will be power drop of the 12V supply, but using heavier wire (#22 or larger) for the power and ground will alleviate that issue.
Note that for #14 wire, the drop is 1.7 volts to the distribution point.