I found a easy way to avoid the ding ding ding at startup. On my truck, if I close the door and buckle the driver's seat belt before I turn the key, it won't ding at all, just starts.
It does take me a few seconds longer to get going. If I am in a hurry, I have the key on before I even climb in, so the glow plugs are warming while I climb in. By the time I am in and the door closed, I can fire it up, and while I wait for it to build oil pressure, I can buckle up. But if I am not in a hurry (or the truck is cold and I will be waiting for it to warm up anyway), I will get all strapped in before I touch the key so it doesn't ding at me.
More on topic, I am surprised that your integration module adjusts the ding volume by adjusting the entire amp gain, instead of adjusting the volume of the chime sound it feeds to the amp. I think that is the real root of your problem there. Though I don't know if anyone makes a better integration module, so maybe you're SOL.
