I think this can be analyzed as a combination of two devices. The first is a ♯ivm7♭5 chord, and the second is iii → biii → ii movement.
One function of the half-diminished chord (m7♭5 chord) is to serve as a chromatic passing chord, which leads to a diatonic chord. The diatonic chord would simply something like a IV chord, a iv chord, a iii chord, etc. For example, instead of writing Dm7 → E♭dim → Em7, we could write Dm7 → E♭m7♭5 → Em7.
Of all the possible ways to use a half-diminished chord as a passing chord, one of the most common is the ♯ivm7♭5 chord. In jazz, an iconic example of this is in Night and Day by Cole Porter:
In measure 9, we see F♯m7♭5, a ♯ivm7♭5 chord for the key of CMaj. After this, the progression continues almost exactly as your progression from Rodrigues Jr.'s. The only difference is the ♭iii chord. Using the key of C, we have this:
Your Progression: F♯m7(♭5) → Fm7 → Em7 → E♭m7 → Dm7 → G7 → CMaj
Night and Day: F♯m7(♭5) → Fm7 → Em7 → E♭dim7 → Dm7 → G7 → CMaj
The top progression (from Night and Day) is more common in jazz than the bottom progression. The top progression (or a variation of it) can be found in many other tunes, including All the Things You Are, as another good answer points out. But to understand your progression, we have to look at the ♭iii chord.
iiim7 → ♭iiim7 → iim7
As you've suggested yourself, the reason for the iiim7 → ♭iiim7 → iim7 is to preserve the parallel movement of the chromatic minor 7th chords. This sound is more common in funk, rock, and pop music. The first example that comes to mind is Alicia Keys's If I Ain't Got You. The key is GMaj, and repeatedly through the song we hear the progression Bmin → B♭min → Amin. The chorus uses a 16-measure form, and the progression is heard in measures 12-13. For example, the first chorus begins at 1:12, and so the first time we hear the chromatic descending min7 chords is at 1:28.
How to Solo
Descending minor licks sound good over this sort of progression. In fact, many people will simply take a single lick and move it down half steps over each chord. Doing that over every minor 7th chord can sound too mechanical for some, and so many people will limit that chromatic movement of the lick to the ♯ivm7♭5 chord and the ivm7 chord. Using descending Dorian scales sound good for that type of approach. Another way to add variety to descending chromatic licks is to simply change the feel when you reach the iim7 chord. An example I really like is to change from (a) descending chromatic Dorian licks to (b) a C blues sound or a C pentatonic sound. So for the entire ii-V-I progression, I might construct blues licks from a C-D-E♭-E-G-A scale or just use a C pentatonic scale.
Another nice option for soloing is to add the V7 chords and use descending ii-V licks. This is something you hear in bebop quite frequently, and it's a common technique for reharmonizing songs. (This might be planned or on-the-fly. I used to play with a sax player who loved to throw these in and expected the rhythm section to hear and follow him.) For example, in C, the progression would become:
|F♯m7(♭5) | Fm7 B♭7 | Em7 A7 | E♭m7 A♭7 | Dm7 | G7 | CMaj |
There are many examples of chromatically descending ii-V progressions, but one that comes to mind is mm. 6-10 of Blues for Alice:
In a sense, this substitution makes soloing much easier because it's easier to find resolution in a ii-V progression than in descending ii chords. Whether we add the V chords or not, the implied ii-V progress is the reason that Dorian is the scale of choice on these types of descending iim7 chords.