Robert, thank you for the submission. Static harmony like this is difficult to play over. It's because in moving and modulating chords, they create interest in themselves. In two-chord harmony like this, you have the full burden of creating the harmonic interest over each section of static harmony. I think your "What doesn't feel natural" write-up describes very well the things that will improve your improvisation. Rhythmic diversity, space, more syncopation, and doing more with fewer notes. The question is: how do you develop all that?

Part of the answer is by listening to accomplished jazz players like Dexter. Transcribe a solo of his or a portion of a solo that is within your skill range. Dexter, however, is a difficult model to emulate. His subtle use of pitch, his unique sense of time, and his sound. But start with the notes. Can you play the notes Dexter played on a particular solo? Maybe start by singing the solo or part of it until you have it in your ear. Then over a rhythm track of that same song, sing your own solo. Take the sax out of the process. Singing is a more direct connection to your musical mind. Sing using the attributes you mentioned such as space, syncopation, rhythmic and articulation diversity, etc. What does that sound like.

Notice in this solo that your lines consisted exclusively of major and minor seconds. You were basically running up and down scales. That is what comes more easily to your fingers than wider intervals and melodic phrases. THAT is why I encourage you to sing.

Try this: record yourself singing an improvisation over changes. Then play that same solo (or fragments of it) on your sax. That is translating the music in your mind to come out of your instrument. Too many players let the friction of their instrument get in the way of the music they have inside. The limitation of instrumental technique limits what we improvise. Continue working on your technique, and at the same time, listen to the music inside you. Let yourself hear the lines living inside your musical mind. You can build that connection with the right kind of practice.