Playing modes over a pedal tone is going to nail the sound of each mode down, but it can also be misleading in that you can wander around aimlessly within the mode and think you’re really “doing it”.
What you need, though, is to develop a sense of the strong and weak notes in each mode, the color tones of each mode and how each mode resolves to it’s tonic note.
One thing that can help is to play the major scale and get that sound in your ear. Then raise the 4th to get Lydian. Notice how you still have a major scale sound, but that #4 adds a different character.
Go back to the major scale. Then lower the 7th to get Mixolydian. Notice how you still have a major scale sound but that b7 sort of rounds off the edge of the natural 7th leading to the octave.
Do the same with Natural minor. Play it until you really get the sound in your ear. Then raise the 6th to get Dorian. Notice how the Dorian sort of brightens up the somber/serious sound of natural minor.
Go back to the natural minor. Then lower the 2nd to get Phrygian. Notice how the sound becomes more intense, exotic or mysterious. Also notice how strongly that b2 wants to resolve to the tonic note. It acts a lot like the 7th of the major scale, just coming from the opposite direction.
Locrian is the odd duck of modes. It doesn’t really fit and isn’t used nearly as much as all the other modes. You can think of it as a darker version of Phrygian. Switching between Phrygian and Locrian can help you get he sound of Locrian happening.
The next step in this process is to do the same thing but start with major pentatonic. The major pentatonic is Ionian, Lydian and Mixolydian without the 4 and 7. What you do with that 4 and 7 gives you the color tones of each of those modes. Switch back and forth between major pentatonic and each major mode.
The same thing goes for minor pentatonic. Minor pentatonic is Dorian, Aeolian and Phrygian without the 2 and 6. What you do with the 2 and 6 gives you the color tones of those modes. Switch back and forth between minor pentatonic and each minor mode.
So major and minor pentatonic give you the base major and minor notes to work with. The missing notes add the individual flavor of each mode. How much flavor you want to add will dictate how much you lay on those color tones.
The final step in the process is to pull out the chord that is hiding within each mode and play it as an arpeggio. The arpeggio for each mode is the 1 3 5 and 7 of the mode.
For the modes starting with C Ionian, you get:
C E G B = 1 3 5 7 = Cmaj7
D F A C = 1 b3 5 b7 = Dmin7
E G B D = 1 b3 5 b7 = Emin7
F A C E = 1 3 5 7 = Fmaj7
G B D F = 1 3 5 b7 = G7
A C E G = 1 b3 5 b7 = Amin7
B D F A = 1 b3 b5 b7 = Bmin7b5
The arpeggio acts very much like major and minor pentatonic with some slight differences on the major modes. You’ll find that minor pentatonic already has the same notes as the arpeggio for each minor mode.
Play the arpeggio for the mode, then add in the rest of the notes.
All of these drills are to get you hearing the character of each mode as well as the character of each note/interval within the mode and how they interact with the tonic of the mode. Your ability to exploit these characteristics of each mode depends on how familiar you are with these details.