Generally, any instrument works by having a source of initial driving vibration, which has a resonance pattern. In stringed instruments, this vibration is usually small enough that it requires amplification, which is done by geometric coupling to a larger vibrating surface. During this process, the body of the instrument either dampens or enhances vibration at certain frequencies.

In reed instruments, I don't think amplification is not so much a consideration. But I think the tone generator - the reed - produces a sawcut rather than a sine wave, and of course the mass and flexibility of the material will affect the initial overtones. Bottom line -- yes, brass and normal steel sound different, and yes, it may be possible to make a steel with properties close to brass, if you try. But I think it will take an effort.

Since you already have a loud tone, the question as to other materials is how much damping occurs and at what frequencies. Again, this is a matter of mass and flexibility, and probably to a lesser extent geometry. So type of wood, metal v wood ends, bellows material, pan geometry -- all have an effect.

The real question is whether the effect is important to the final perceived sound. For instance, I'm sure balsa wood (high damping) would sound very different from mahogany. But whether most people could tell the difference between mahogany and maple, I don't know. Similarly, while I'm sure there IS a difference in sound created by different pan geometries, I suspect it's so small that it's overwhelmed by other factors - Iand may not be anything most people could hear anyway. Sounds like a research project to me.

I know I haven't actually answered the question at all. But I thought it might be useful to toss about the actual mechanism of sound production.