I would contact a local interior shop and ask them what they use or if you could rip out the carpet and take it to them.  It is also pretty cheap to get a replacement carpet and you can choose from a variety of colors.  Not just factory colors.

I heard -at least with seat dying, the fibers become "harder"

I would recommend replacement carpet- if you can afford it (like crimsion said, late model has allot of affordable options)

I would also go with replacement carpet instead of dyeing.