>The input to this was "1.5~3 x 0.9~1.0 x 0.1~0.4 x 0.1~1.0 x 0.1~1.0 x 0.1~0.2 x 304~10000" - every single range was positive, so regardless of what this represents, it should be impossible to get a negative result.

Every single range here includes positive and negative numbers. To get the correct resulting distribution you have to take into account the entire input distribution. All normal distributions have a non-zero possibility to be negative.

If you want to consider only the numbers inside the range you can look at interval arithmetic, but that does not give you a resulting distribution.