Very good demonstration & explanations. I used to play tenor trombone & alto recorder in a Renaissance band. What this demonstration shows is that in the absence of an available authentic sackbut, that a decent sounding tenor trombone will probably suffice, in my opinion. I had considered purchasing a cheap 2nd-hand sackbut, but because so few of these instruments are manufactured & sold brand-new, I couldn't find anything affordable that was available used. If you want to appear authentic to your audience, you could simply dress up in authentic Renaissance garb...George, Canada...
The Bass & Great Bass (aka Sub-Bass) Sackbut Trombones had a Handle on the Slide to help w/ moving it back & forth. It's a Type of Trombone (Italian for Big Trumpet or Bass Trumpet) cause you slide the slide back & forth to change the pitch.