Is it possible to (safely) make dry instant rice?
Typically dehydrated foods of this sort are freeze-dried rather than dehydrated by heating. This is a process of sublimation of the water out of the food in a controlled manner under very low temperature conditions. This is generally not practical at home due to the nature of the equipment needed.

However, it seems that the instant rice is dehydrated in ovens. I suspect that you could do it with quite a bit of experimentation by spreading rice out in a thin layer on some baking sheets and heating to around 60 Celsius until dried. This should be hot enough to prevent most bacteria from growing successfully. As you have used the commercially prepared versions before, you already know the texture and how you would prepare it after drying, so you could play around and see.

Personally I like to use instant couscous when hiking - it rapidly (1-2 min) hydrates on addition of just boiled water, and like rice is readily available, easily measured out into aliquots for pre-packaged meals, and can be transported in a package with salt and other dried ingredients for a rapid and filling meal.