Helmut,

You wrote, "What do you think about adding a reverse
gearing box on the axles? Is such a box available?"

This was done on some very early cars about 100 years ago.  I have a book with
lots of illustrations that shows some of these complex drive systems.  Yes
it's possible.  No, it's not a good idea.  They weigh something, and if it's
added to the unsprung weight, it would really negatively impact the suspension
performance.  Also, they would be another wear/breakage problem area.
Finally, gear sets typically transfer about 97% of the input power and convert
about 3% to heat.

Nice thought, but it's got too many downsides.  Sorry.
John