First of all,.. I didn't listen to the backing track,.. So I suppose you are correct about the chords.
Abm7 - Db7
I like to simplify when thinking about what to play:
( from here on, think down 1 step

)
Am7 - D7
In notes :
A C E G and D F# A C
You could play Em over the whole thing : E F# G A B C D E
Or Am pentatonic : A C D E G A
Or play with the chords:
A B C D E F G A over the Am7
D E F#G A B C D over the D7 ( note the C !! it's D mixolydian (= Em))
Or just play the arpeggio's all over : A C E G and D F# A C
There are about a million other options I guess, but the most important thing is focusing where you end a lick or phrase. You can play the most amazing lick ever invented, when you end on a note that wants to resolve to another it's not going to sound "easy". Ending on the 1,3 or 5 of the Am7 or D7 will work fine. Mix it all up, play outside, go chromatic, go wherever you like, but make sure you end on the right note.
Another great exercise to come up with interesting things is to think of a little phrase or lick in your head, imagine how it sounds and then play it. This usually makes for more musical phrases instead of "finger-fueled"-phrases.
My suggestion on tackling this improv:
Listen to the track, KNOW where it changes from Am7 to D7.
Play the chords.
Play the arpeggios.
Play the scales.
This way, you know what's going to happen ( listen )
You know the chordal notes ( play the chords )
You know the chordal notes all over the neck ( play arps )
You know the scales you can use ( play the scales )
Experiment, keep your ears open, record and listen back.
Edit: In retrospect, in thought you might have wanted a suggestion instead of a million options:
I would go with a mix of the following.
Am7: Am scale and Am arpeggios, with some Am pentatonic when I'm lazy and/or want to play it safe. When the D7 kicks in, I'd start off on the F# note. The note hasn't been heard before and therefore has a nice effect. Then continue in Dmixolydian and D7 arpeggios . At the very end of the D7 chord I might briefly play a G# ( maybe in chromatics: F#, G, G# ) to resolve to the Am7 chord.