Whoever told you that a brushless motor drains power faster is talking rubbish.
Brushless motors are much more efficient, so for the same motor power a brushless motor will run for longer on your nimhs than a brushed motor will. Stick a high power brushless system in your car and your nimhs will drain fast, but the equivalent brushed motor will drain your batteries even faster. Brushless systems will work fine with your nimhs.
After saying that, if you already have a brushed system then the cheap option is to just upgrade to another brushed motor, and what motor you want will depend on what equipment you already have as the limits of your ESC will limit what motors you can run.