The gentle agitation you describe is actually TOO gentle, you are at risk to get uneven streaks on your films. You don't need to move the tank like a cocktail shaker, but Kodak's description is quite clear:
"1. Fill the empty tank with developer.
2. Start the timer. In the dark, carefully place the loaded reel into the developer solution.
3. Quickly attach the top to the tank. Firmly tap the bottom of the tank against the work surface from a height of approximately 1inch (2.5cm) to dislodge air bubbles from the surface of the film. Air bubbles can interfere with development and produce low-density circles on the film.
4. Provide initial agitation of up to 5cycles, depending on your results. For KODAK PROFESSIONAL T-MAX Films, provide initial agitation of 5 to 7 cycles in 5 seconds. For an invertible tank, one cycle consists of rotating the tank upside down and then back to the upright position. For a noninvertible tank, one cycle consists of sliding the tank back and forth over a 10-inch (25.4cm) distance. With tanks that have a handle for turning the reel, rotate the reel back and forth gently through about one-half turn at a rate of one cycle per second during initial and subsequent agitation. Steps2 through 4 will take approximately 7 to 20seconds, depending on the type of tank.
5. Let the tank sit for the remainder of the first 30 seconds.
6. After the first 30 seconds, agitate for 5 seconds at 30-second intervals. Agitation should consist of 2 to 5cycles, depending on the contrast you need and the type of tank."
There is no "waiting for the liquid to settle", there is no time to wait if you turn the tank 2 to 5 times within 5 seconds.
I am sure many people would like to see a Youtube video so that they are really sure how to do this. Kodak, you hear me?
BTW, most people I know close the tank and then fill the developer into the tank.