Oh my lord, please for the love of god, if you can't play this song on the double kicks and are trying to learn how, PLEASE, DO NOT try to teach yourself heel toe in order to keep up with the speed. You will only hurt yourself in the long run.
This song is relatively easy, but as you said, can get tedious on the legs. You need to practice playing with a metronome. I know you've heard it plenty of times, but go to any serious drum forum/talk to anyone who has been playing drums for an extended period of time and they will tell you the same thing. Drumming isn't something you can pick up overnight, techniques and methods that some drummers used may not work for others, and as such you need to learn for yourself (this is what makes every single drummer unique!).
There are certain things you can modify that may help, not only with speed but endurance. Try readjusting your double kick pedals, there (usually) are many settings on a double kick that need tweeking, no double kick comes stock and ready to play for everyone. If you're not sure what all the features are (I know when I first started using double kicks, I had no clue what to change/adjust) google is your best friend. Just type in your pedal and I'm sure you'll find someone who has your pedal that is in the same predicament as you. You may also want to look into getting different beaters, or even adding/removing weights to them.
Another thing you may want to look at is your base drum and how it's tuned. Adding/removing pillows/blankets to get the right rebound and/or tightening the heads play a key factor in the rebound of your pedal, and can not only help you with speed/endurance, but can ultimately make your base drum sound WAY better!
Hopefully some of these tips will help, and if not, just keep practicing it! You'll get it eventually!