It might not be so practical, but I'm remembering... I don't think stacked chords that are higher will be inverted that often, so that helps. On the piano side, you might not play the bass note though. Solo, yes. Jazz combo, no, probably the bass has the root and the pianist has the third or seventh.
Either way, still good to know for learning. One way to simplify it is thinking of two different chords. You only need to think in terms of triads or seventh chords then (adding this other level by combing those). ex. A dominant 13th, #11 is a dominant seventh chord plus a major triad built on the second step of a major scale built off that root note... ex. C dom 7 + D Maj triad.
To think more that way, it can be helpful to be able to play triads on each step of the scale (diatonically, although in minor you raise and lower the VI and VII chord/note areas to make it sound better, going up and down). Being able to play seventh chords or major and minor scales. Being able to arpeggiate triads and seventh chords.... Or maybe playing 13th chords diatonically over major and minor scales. I don't think I've tried is, but the 13th will get all the notes of the scale/chord.
Knowing how the "lower scale" intervals line up/match the "extended" scale intervals helps. ie 2nd = 9th, 3rd = 10th, 4th = 11th, 6th = 13th, etc. (They do match, but it also matters how you think about them, where they are in an actual chord, how it actually sounds... Someone could easily argue that a 6th is nothing like a 13th, which is also true.) And it depends how an actual chord actually functions
And then there are common voicings of the chords. Some notes are left out. For understanding, knowing/seeing/understanding them all is probably helpful. I don't know the standard voicing for all those.
And then in reality there are also suspended chords, added note chords, etc.