You can also vary the rhythm and articulation. Also look for 'common' chord notes between the 'changes' or where you can drop or raise a semi-tone with a leading note as you move from one chord to another.
Another good trick to really get it ingrained is to play the chord tones in sequence (1,3,5,7 or whatever is called for) through each bar. Then go back and play them all in first inversion - so you start on the second note of the sequence (so you'll play 3,5,7,8 - 8 being the root note an octave higher). Play each chord in this style. Then do them in 2nd inversion (5,7,8,10 - 10 being the 3rd raised an octave).
So, using C7 as an example, play C1 E1 G1 Bb1, then play it in the pattern E1 G1 Bb1 C2, then G1 Bb1 C2 E2, finally Bb1 C2 E2 G2.
Once you're bored with that mix up the inversions - bar 1 starting on root, bar 2 on 1st inversion, bar 3 on root etc. Just see what fits - you'll find the common or near tones starting to show themselves to you, and you'll find one inversion naturally follows neatly the chord you've just played.
And then mix up the order of the notes by perhaps playing the first chord in 'normal' pattern (1,3,5,7), then play the next chord from top note of chord down (7,5,3,1), and then back to 1,3,5,7 etc. It's tricky, take it very slowly, but believe me it will really help you to get it fixed in your head and fingers.
Having done all that you'll have broken the habit of playing a scale or chord from root upwards. If you only ever do that it will be reflected in your improvisation, whereas using different inversions allows you to weave a melodic path through the progression without the saw-tooth effect of returning to the root note at every change.
Sorry if that's a bit lengthy, it's not a quick fix, but spend an hour just working on say 4 or 8 bars and it will start to click into place. And you'll begin to hear and feel the progression.
Do it
without writing out the notes as soon as you can.
Phil