If you approach modes only from the conceptual side you'll never get it.

If you want to be able to hear modes, you have to practice listing to modes.

If you want to practice listing to modes you need a truly modal instrument. In the US the most common modal instrument is a traditionally fretted (no 6 1/2 fret, no 1 1/2 fret, etc.) lap dulcimer.

So, buy or borrow a traditionally fretted dulcimer. Tune it into a mode. Whack away at it. Be sure to fret ONLY the melody string. The remaining strings are intended to be constant drones.

Stick with the old common tunes. Old Joe Clark. Soldier's Joy. Shady Grove. All their notes will be there on the melody string.

Try the same tune in different tunings. Each tuning changes the "character" of the tune in significant ways.

Listen, listen, listen.