I have programmed in the mod wheel at the beginning of the session so that I don't have to manually do this, but.....the instruments are still mute until I manually touch each mod wheel, 32 voices total.
I just tried to recreate your problem, of course not with 32 instruments. I couldn‘t create exactly what I think you meant, but here are a couple of simple things. These are simple concepts, but they might be overlooked:
One needs to place a modwheel setting on a midi track for each of his/her 32 instruments, not for each instance of the Kontakt player. Since each instrument responds to data without affecting others, you can‘t get away with just some data in a track for each instance of the player.
The Kontakt player will remain almost silent until you press the play button and the wiper passes over this data. Once this occurs, that instrument in the player will sound either from your midi controller or by pressing a key with the mouse on the player‘s keyboard.
All this means that if you quit your project and load it again at a later time, you will get little response from your instruments until you press the play button and the green wiper passes over their respective data. Once this happens you can press the keys on the Kontakt player and hear the note played at the setting you entered on its track.