How to change the volume of an specific instrument midway through the score without using dynamics

Make it another instrument by using the "Change Instrument" text and choose to change to the same instrument.

Although I don't get your aversion against using a dynamic for this; a thing that is entirely designed to and intended for letting a player know at which volume it should play. You can set the velocity for a dynamic using the Inspector, making it a very precise thing as well.
And indeed, for some instruments, playing them softer/louder does result in a change of timbre as well; inherent to how the instrument is fabricated. Some soundfonts indeed contain several velocity layers, some don't and only use one velocity layer.

Indeed, using the mixer for this is wrong, real musicians playing the score won't see the dynamic, And real instruments do change sound as they get quieter. As for precision, you can set velocity of the dynamic in the Inspector.

About the only case I could see where using the extra mixer channel trick would make sense is if the instrument in question is meant to represent an electronic synthesizer that actually has its own volume control, and you wish to have the player turn down the volume at that point rather than actually play softer. In that case, he, use the change instrument, and maybe change the text to tell the player what volume level you want to change to.