Noodler,
Both of these progressions do sound good and they would both work with
Ain't Misbehavin'. But in this case, we are dealing with 2 different progressions that are moving in different ways to arrive at the same spot.
The progression I gave you is being driven by the bass line, C-C#-D#-E. The one you wrote starts that way C-C#-D then moves from D to G via the Cycle of Fourths.
The D#dim7 is not substituting for G7. It is, instead, functioning as the V7 of a
substitute for the I chord. That's why they don't have common notes.
In harmony, there are 3 sounds. Major, Minor & Dominant. There also 3 Functions. Tonic, Sub-Dominant & Dominant.
The progression C-C#dim7-Dm7-G7 would end on C. G7-C (V7-I) is a harmonic inevitability in tonal music.
With C-C#dim7-Dm7-D#dim7-Em7, the last chord, Em7, is functioning as a substitute for C.
CMaj7= C E G B
Emin7= E G B D
So, in this instance, Em7 functions as CMaj9.
Harmony is a big subject. Any time you spend studying it will pay off in large dividends.
Hopefully this is clear. If not, shout back with questions and I'll try to clarify.
Regards,
Monk