So instead of taking the ahead position, multiplying with the inverse of the view matrix, then using it in the model matrix, we do it in a slightly different order: Take the ahead position, plug it into the model matrix and then multiply with the inverse of the view matrix.
I finally understood what you mean by "plugging in". This means "translate" the model matrix by the aheadPosition. It took a while to figure out.
The object is now placed in front of the camera. Thanks again for your help!