Don’t worry about the criticism of Goenka’s technique you refer to. I think you mean the sweeping through the body part of Goenka. You will find a form of this in the visuddhimagga in reference to the 32 parts of the body and skin where a pattern of sweeping the body is found.
But I digress. The 4 elements meditation as taught at Pa Auk is described in the pdf. U Subhuti linked to. But I am here to tell you there is more that can be done with 4 elements than is there.
Firstly once you become adept at discerning them in depth. Hard, rough,heavy, soft, smooth, light (earth), flowing, cohesion (water), heat cold (fire), supporting, pushing (air) or even if you only have a limited comprehension of them you can use then when doing exercise.
I use them when running, swimming and walking. I just rotate through earth, water, fire, and air at my leisure. Then develop perception that they are not me, not mine, not self. I sometimes hold on one element for a lap of a pool or for a period of time, then move to the next.
So you can use them when sitting, walking, lying down or whenever. It is very rewarding.
I can also do 32 parts of the body like this as well.
So one of the issues with all the techniques is that they ignore the majority of your life which is when you are not sitting. You can do meditation snacks on elements or the 32 parts at any time and it will deepen your perception of either.
Also 4 elements and 32 parts of the body can be very close to each other and assist each other. 4 elements maybe broader and 32 parts closer to your sweeping method.
In the end the goal is to see reality of impermanence, dukkha and not me, not mine, not self.
Based on 5 precepts and an understanding of kamma it can take you to an end of suffering in body and mind.
Good luck.