After getting comfortable with inverting the chords in their most basic form, I then get my students to add the prescribed extensions in place of the least colourful notes in the chord. Most of the time, we see the 9 (flat, natural, and sharp) replace the root, and the 11s and 13s replace the 5th. At this stage, we are only using the extensions that are on the page.
After those extensions are learned, then it’s time to create rootless voicings. We replace all of the roots with some form of 9. I find that this is a good way to start hearing the colours of the 9 on strong beats, as opposed to hearing it as a passing tone that needs to resolve.
Here’s an example of my playing over The Days Of Wine And Roses with rootless voicings, and the added extensions.
Here are the PDFs of the new voice leading.

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