I quite agree that sound waves don't reflect on the walls, "resonators" etc. They're far to long.The surface of the 'resonator' is going to be reflective- but from the standpoint of wavelength,
even the largest keys on a bari are sitting at about 5khz, so they are going to have limited
effect on the spectral content of what's coming out of the body or the bell.
However, if you think about things at the right scale - it's statistical mechanics. The wave along the instrument describes the (offset from atmospheric) pressure, pressure is "average" kinetic energy and energy clusters around the resonances (tone and overtones). But that's only stable so far as the walls are ideal - perfectly elastic. If molecules lose energy when colliding with the wall, they'll lower the pressure a bit, effectively contributing to other partial frequencies.
If you fall for that story, pads are - compared to brass - much less reflective for air molecules so you should get more energy spreading out to partials and higher overtones. Putting reflectors over pads should reduce the amount of energy leaving the fundamental and lower overtones.