I've been studying modes recently and since I have a piano, tried to experiment with them by improvising simple tunes.
My problem is that as soon as I use something else that Ionian, my perception of the key immediately shifts. As an example, I've been experimenting around C Lydian.
Initially, to establish the C root as strongly as possible, I do a series of V-I cadences, avoiding II, ivº and vii which contain the F# "lydian" note. At this point, the chord of C major definitely feels home. However, as soon as I start adding the F# note, or a chord which contains it, such as D major or B minor, the home kind of immediately shifts and becomes G major (while C major now feels like an unresolved IV), which is telling me than I'm essentially now playing in the key of G major.
At this point, if I redo a series of I-V-I then I can re-establish C major but I never manage to get this C Lydian feel. It's always either C Ionian or G Ionian, alternatively.
What can I change in my improvisation (or in my hearing) so that it can feel being Lydian with a C root/home?