I personally like to place a knee on hip, and drive forward...
It's a good wrinkle i think.
Another thing i sometimes see people getting mistaken about is the idea that you need to keep the guy flat to do the choke.
What you do absolutely need is to pin the guy's
far shoulder on the mat to make the choke easier; his
near shoulder however, does not need to be on the ground, and indeed, it can actually be better if it's off.
If both of the guy's shoulders are flat on the mat, then the axis for smushing his neck and shoulder together is more or less sideways. This can still be done with the right methods (see how Ryan Hall or Braulio Estima often teach arm triangles, by almost literally turning sideways themselves to project their their chests into the opponent's shoulder), but it can be awkward and not immediately intuitive to new users. It can also sometimes result in trade-offs; if you use more of your force to keep the guy down, thats less force going in the direction of the choke; if you use more force going sideways into the choke, that's less force going down to keep them pinned.
On the other hand however, if the guy's near shoulder comes up, that changes the angle the right axis of force goes through relative to the ground; the nearer it goes up to an angle, the more the direction of force through the axis of the choke also goes down into the ground, increasing your ability to keep him pinned as well, allowing you to better synergize your forces.
Moreover, by changing your angle in this way, it also lets you engage more of your large muscle groups into the choke, where otherwise if they were flat, your leg drive might not be exerting as much force on the right axis, with some of the effort simply putting pressure on muscle or bone tissue rather than vitals (which is why many who teach the 'sideways' method of the choke teach you to sort of 'collapse' into it like deadweight, so you don't waste effort and just let the structure of the hold do the work).
You can see shades of this in how Renzo demonstrates in the video. A more explicit variation of this principle is shown here by Rob Khan.