I think I've done it

Hope it is right, because I've never gone with "only 7 chords" approach, so some progressions sound weird to me
IonianCharacteristic notes - don't really know

Imaj7 - IVmaj7 - V7 - Imaj7
Amaj7 - Dmaj7 - E7 - Amaj7
LydianCharacteristic notes -
#4 = D#
Imaj7 - II7
Amaj7 - B7
MixolydianCharacteristic notes -
b7 = G
I7 - bVIImaj7
A7 - Gmaj7
AeolianCharacteristic notes - b3, b6, b7 = C, F, G
Im7 - bVIImaj7 - bVImaj7 - bVIImaj7 - Im7
Am7 - Gmaj7 - Fmaj7 - Gmaj7 - Am7
DorianCharacteristic notes - b3, b7 (or only
natural 6 if compared to aeolian) = C, G (E)
Im7 - IIm7 - Im7 - bVIImaj7
Am7 - Bm7 - Am7 - Gmaj7
PhrygianCharacteristic notes -
b2, b3, b6, b7 (or only b2 if compared to aeolian) = Bb, C, F, G (Bb)
Im7 - bIImaj7 - Im7 - bVIIm7 - Im7
Am7 - Bbmaj7 - Am7 - Gm7 - Am7
LocrianCharacteristic notes -
b2, b3,
b5, b6, b7 = Bb, C, Eb, F, G
Im7b5 - bIImaj7
Am7b5 - Bbmaj7
Hope I got everything right