Piazzolla did compose some guitar material, his "Tango Suite" for two guitars written specifically for Sergio and Odair Assad. The second movement is my favorite:
https://www.youtube.com/watch?v=TNDlnNnxfhw
Carlo Domeniconi's "Koyunbaba" is another guitar piece I've always really liked, performed here by the not-Star-Wars John Williams:
https://www.youtube.com/watch?v=TNDlnNnxfhw
And of course other greats like Villa-Lobos, Tarrega, Granados, Albéniz, etc.
I do realize the singular devotion and training that is required to reach the highest levels of classical guitar playing. It's astounding! My dad took master classes from Eliot Fisk (whose playing I don't really like that much) and got the opportunity to play in front of Julian Bream a few times (whose playing I DO love).
Thanks for that nice performance of Lute Suite #4. It was my mom who instilled in me an early love of Bach. If you've never heard Angela Hewitt or Alicia de Larrocha playing Bach, then I'd highly recommend checking them out!
And damn, your teacher is a ferocious guitar player. Both pieces are great!