The basic concept
Speaking broadly, the point of the bebop scale approach to block-chord harmony is that you don't have to think of a different chord for each melody note. For a major chord, if the melody note is the 1, 3, 5, or 6, you play a major 6 shape (C6), and if the melody is the 2, 4, ♭6, or 7, you play a diminished 7 shape (Bdim7).
The result looks like this. I have put the voicings in close position, assuming you know how to drop the second voice to make it match yours:
Note that in Barry Harris's conception a "major" chord is a major 6, and the 7th scale degree or leading tone is a non–chord tone. If your example had a prominent B on a downbeat, then I would harmonize using a Cmaj7 shape or something similar. But this would be somewhat beside the point, because the context for this discussion is, how do we harmonize a melody built from the bebop scale? The principle of bebop scales is that only chord tones appear on downbeats, so if a melody is written purely using the C major bebop scale, you will never have B (or D, F, or A♭) on a downbeat.
That is to say that the chord voicings Harris is teaching in this video aren't meant to be a comprehensive formula for harmonizing any melody. Any real melody will have some parts that can be interpreted as coming from the bebop scale and others that can't; these voicings apply only to the former.
Also note that for other qualities of chord, there are other bebop scales. The dominant bebop scale is the most important one after the major bebop scale here. These scales also yield two-chord alternating harmonic patterns that can be used to harmonize melodies that use the scale.
I've discussed these considerations on this site before here, but let me excerpt a relevant part:
A different set of voicings, derived from the appropriate bebop scale, is used for each chord. Over the I chord, the voicings come from the major bebop scale and alternate between the major I6 and vii°7 chords. This is because the stable scale degrees (1, 3, 5, and 6) tend to sit on the downbeats, so we'll hear the sound of the I chord on the downbeats and a passing chord, vii°7, on the upbeats. This principle of alternating between the main chord and passing chords is central to Barry Harris's harmonic concept, and also used widely in big band arranging.
Over ii and V, we generally use the mixolydian bebop scale. In C, that's G A B C D E F F#, adding a major 7. The two chord shapes outlined are G7 and F♯ø7, and a well-constructed melody usually again has G, B, D, and F on downbeats, so the F♯ø7 acts as a passing chord. (Occasionally, one note can be swapped around in order to create smooth voice leading; changing the E here to a E♭ to form F♯°7 is a natural choice.)
There is also a "melodic minor" bebop scale; here I have written out the voicings for a Cm6 to parallel your second line. It's nearly the same, just changing E to E♭:
As for practicing these voicings, I would recommend doing as you have done, writing out the voicings in both close and drop-2 (and maybe drop-2-4 as well) forms, and practicing walking up and down the major scale in various keys. The goal is to get to a point where just looking at the keyboard, you can "see" which notes belong to the "chord tones"/major 6 subset of the bebop scale and which ones belong to the "non–chord tones"/diminished 7 subset. Then the rest of the notes in the voicing just fall in place below the melody.
What's happening in the video
At the point in the video you have linked to, Harris is introducing a more advanced application of the bebop scales that disregards the "alternating chords" principles outlined above. Your transcription is correct, but you should note that that set of voicings is just one of an arbitrary number that you could generate by picking any shape from within the bebop scale and moving each voice up and down in diatonic parallel. Rather than getting hung up on playing that exact line, developing the mental dexterity to walk through the bebop scale using any shape would be a better practice goal.
The editing of the video makes it easy to think that this follows directly from the "basic" bebop scale harmonic conception, when in fact there are multiple things going on: Harris is treating the bebop scale as a mode, and applying another harmonization technique, namely, the technique of moving a shape diatonically through a scale or mode, to it.
So (and this is just my opinion), I wouldn't ascribe special significance to the chord voicings you have transcribed. Rather, we have one concept (bebop scales) and another concept (parallel diatonic harmonization) and they are being used simultaneously.
When someone says "bebop scale harmonization," they are usually referring to the more narrow process outline above.
