Not sure if you wanted comments, and also don't know if that would include suggestions. But if I've stepped over the line then you can say so.
You've got a good concept of lyrical playing and the potential for being a good melodic player. As it is this is currently manifest as playing up and down the (correct) chord's scale with slight hesitations and accents. That's a good start and your feeling for the tune is very sensitive/fitting. The next step is to make this your own. Unfortunately there is nobody (that I know of) who can teach melodic creativity. It can be encouraged, but the last thing that should be done is for anyone to blindly copy melodies. To be valid it has to come from you and be your own voice. Most everyone can judge what makes a good melodic line, but it's often hard to define. In simple terms it's often something that "sounds right". It's often thought of as "catchy" and can be remembered by non-professional listeners who might hum or whistle it after just one listening. Common devices are repetition, tension and release, and climaxes, which can be studied, but IMHO (as in specific melodies) shouldn't be copied. It's a common trap that students can fall into when studying any of the creative arts...being so enamoured of what's already out there that they just copy those things without creating anything of their own. Listen and absorb and try to understand what makes melodies work without getting trapped.
An often mentioned method for developing melodies is to sing what you would play. It shouldn’t be surprising that this may not be anything like what you may have played on your horn. Singing MUST come from you, whereas sax players are too often taught to just play changes, which is often diddling within the chord structure and usually not melodic. Being able to play what you would sing is to be one with your instrument. That IMHO is what it’s all about. If it’s not coming from you what are you offering up?
