Hey Christian 
Great question, here are a couple of ideas:
Introduce the Dominant IV Chord
It can be nice to play the Imaj7 chord, then move to the IV7 chord, which can then be used to fall down chromatically into the iii-7 which starts the 3625 progression, this is what I play in my lesson on “the most beautiful chord progression” :
I was chatting with a student about this progression recently, and one of the things that makes this progression so nice is how the melody interacts with the voicings.
If we just play the voicings it can sound a little plain and so targeting the ‘pretty tones’ such as #9 over the III7 chord (G7#5#9), the 9th on the vi-7 chord (C-9), the 9th on the II7 chord (F13), adds interesting colours over the chord voicings. The top note of the voicing is the one that shines above the rest.
In particular, notice that I target these tones with diatonic, chromatic, and arpeggio-based approach patterns which add much more melodic interest to the progression.
Approach the iii-7 Chord with its 25
This steps outside of the strictly diatonic harmony because if we build a 25 progression into the iii-7 chord, we could then have a progression such as the following:
#iv-7b5 to VII7alt —> moving into our 3625 (remember that the diatonic 3 chord is a minor 7 chord and so I approached it with its minor 25)
A really nice example of this progression is what Beegie Adair plays here for her intro to the tune “Body & Soul”:
I loosely transcribed what she plays and tweaked some of the chords to my own taste and I ended up with the following progression:
G-11b5 → C7alt → F-7b5 → Bb13sus / Bb7#5 → Eb-9 → Ab7alt → Dbmaj7 → Bb9sus / Bb7#5
The numerics of this in the key of Db Major would be:
#IV-7b5 → VII7alt → iii-7b5 → VI13sus / VI7#5 → ii-9 → V7alt → Imaj7 → VI9sus / VI7#5
This is to set up the Eb-7 which is the first chord in the tune Body & Soul (In Db Major) and so she adds an additional VI7 chord after the #4-7-3-6-2-5-1 which sets up the ii-7 to start the tune.
Some interesting things to note in her introduction are:
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the -7b5 flavour used over the minor chords
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the sus chords moving to altered dominants that she plays twice for the VI7 chord
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targeting the ‘colourful notes’ such as the #9 over the Ab7
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how her left hand commands a lot of the piano through the arpeggios she plays
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her right hand melodies, arpeggios, and approach patterns
You might like to check out the 5th chapter of this seminar where I outline the approximate harmony and melody she is playing:
What I explain and demonstrate is not 100% accurate to what Beegie plays, but certainly the overall vibe of the intro, the chord colours/tensions used, the sus movements etc… all heavily reflect her intro.
Practice Tips
Check out the lesson/seminar above, also also listen to how your favourite players set up their tunes as often they are using diatonic progressions such as 3625s with some of the tweaks mentioned above.
Drilling the basic 3625 progressions during practice sessions is a great idea so that we know the chords and so that we can visualise them and find them on the piano.
The next step is to add melodic interest over the progression and this is best learnt and absorbed from transcribing something that we personally like (the Beegie Adair intro above for example was something that piqued my interest) and then transposing it to different keys.
Then when we play these progressions we ‘internally hear’ the melodies and the ‘melodic pathways’ from the recordings that we have spent the time to transcribe and transpose, and it naturally comes out in our playing.
I hope that helps and have fun working on this stuff! 
