Glenn sounds absolutely spectacular in that recording, as usual!
As far as I know pieces of this sort are usually simply referred to as "unaccompanied" (please correct me if I am mistaken!)
Here are a few different unaccompanied euphonium solos, with links to recordings:
David Gillingham - Blue Lake Fantasies: Mvt. 1 Mvt. 2 Mvt. 3 Mvt. 4 Mvt. 5
Yo Goto - A War in Wonderland Mvt. 1 Mvt. 2 Mvt. 3
Nicholas Falcone - Mazurka video
Sunao Isaji - A Trip Around WakuWaku Island video
Chris Dickey - Movere video
I'm looking forward to hearing more about the project you mentioned!
Willson 2900 TA-1 Euphonium - Denis Wick 4AM
Yamaha YSL-643 Trombone - Bob Reeves BrassArk 5G "Gladstone"
Yamaha YSL-8440 Trombone - Denis Wick 5BS
VMI 3301S BBb Tuba - Schilke Helleberg
Past:
York Preference 3067 Euphonium - Denis Wick 4AL
Benge 165F Trombone - Benge Marcellus
Wessex BR140 Baritone - Denis Wick 6BS
F.E. Olds Special Trombone (ca. 1941)