You're asking for the wrong thing. Don't ask for scales and modes for selecting notes randomly, as if that was "jazz". It's not jazz, it's just dumb and it sounds like what it is, random rubbish. The tune in question is not modal anyway, it has an actual chord progression.
- Find out where the tonic, i.e. home note is in each section of the song, and is the home chord a minor or major chord? What's the key? The song changes keys a few times, sometimes temporarily, but you'll notice this when you find out what the chords are.
- Find out what chords are played on the recording, and how they relate to the tonic. And how they relate to the basic scale of the key - there are occasional temporary modifications to the scale on the recording.
- For each chord, keep track of where its notes i.e. root, third, fifth and seventh are. If you play guitar or a solo wind instrument, it helps if you play the chords as arpeggios.
With this knowledge, you'll be able to build solo lines from the chord tones. After you can play chord tones along with the song, start adding non-chord tones between chord tones.
I'm not sure what you mean by "intermodal transitions", but you have to be able to make chord substitutions and alterations in your mind and arpeggiate those chords. For example, substitute a dominant seventh chord with a minor (or minor seventh) chord rooted a fourth below it, e.g. instead of A7 play Em7. Or a ninth chord a tritone above or below the chord, e.g. instead of A7 play Eb9. Or play aC#dim7 in place of the A7. Or overlay an F#7 on top of the A7. Or a Bb.
When you can do the above, you'll start to develop a sensitivity to harmony and possible notes at each moment - where the tonic feels to be at each moment and what harmony progression you're implying, and how your choices change the situation. And then you might be able to see different scales that might be layered on top of the chord changes - there are many possible scales, they can change many times inside a single bar, and each possible scale means a set of possible chords. For example in a song that's in D major, and when there's an A7 dominant chord in the basic harmony that you're jazzing up, you can see an A half-step/whole step diminished scale there ... which happens to contain the A dim7 and Bb dim7 chords ... and the F# major chord too. But you don't have to think of an entire scale at all, because you won't play all of it at the same time anyway. What you don't play, is left to imagination.
However, if you cannot feel where the chord root is at each moment in time, and how different played notes and chords change that feeling, then what sort of jazz could you possibly play? Random rubbish, IMO.
You can start practicing the chord-soloing and chord substitutions even without being able to instantly identify the chords by ear. Use a song book that has the chords figured out and written for you.