Great question here @nickedwards and welcome to the community area.
I have recorded a few different takes on this section showing some possibilities to add harmonic interest using inner voice movement, and passing chords.
Take a listen to the recordings and read the explanation and try to follow along by listening to the recordings I have made. This will be a nice listening exercise. If you’d like I can also notate these for you but try listening and working them out with your ears first
Also check out the related lesson and seminar links.
Inner Voice Movement
The device is very simple but also very effective - Inner Voices:
More specifically, I am simply moving the 5th to the #5 in the first bar of F (just a half step movement but it adds a lot of interest), and then in the 2nd bar I play 5 to #5 to 7 to 6. I also play these inner voices with both hands to create a bigger sound.
Learn more about inner voice movement in the following lessons and seminars:
This is quite a big area of study, and so I have recorded 3 variations here, from simple to advanced. I also combine the passing chords with inner voice movement so remember that these devices do not exist in isolation.
Here is the first example:
Here I move to the V7 chord of F major which is C7, so instead of just 2 bars of Fmaj7, we now have a quick transition to the V7 chord and back to F:
Fmaj7 - C7b9 / Fmaj7 (with inner voices)
then I add the E bass note which leads to the D-7 in the next bar.
Think what is coming next…
If we think of the next bar (D-7) which is cut off on your screenshot, we can add some approach chords to the D-7, so now instead of 2 bars of F we have:
Fmaj7 / E-11b5 - A7b9 (the 25 of D-) here is how it sounds:
Finally to take this a step further, we can harmonise the melody notes in the 2nd bar of F which lead us to D minor: