Hi @scott1, thanks for writing!
First, always remember what function the chord has; in this case the difference between the 6/9 and the 13 chord is that 6/9 chord is functioning as a tonic (I), whereas the 13 is a dominant (V).
So, when you’re practicing chords, always remember that the only important notes of the chord are 3, 7 (or 6 in the case of 6/9) and the root, for example:
So, when you approach more complicated chords from this angle, you will begin to understand harmony better.
How to practice to become faster in playing the 6/9 chord when seeing it on a chart.
First, always think of it as a tonic, or as something that is steady.
Play simple 3-note voicings in every key using only 1, 3 and 7 or 6, here example in C, with both inversions:
After you are totally comfortable with this, you can add the 9th to the chord, again with 2 inversions:
The main point being; Learn to hear and understand the core of the chord first before the extra tension (9th, 11th 13th etc.).
This way you will build up your knowledge from the foundation of functional harmony, and this will help you with every step on the way.