We did this route in December 2005 and the FCO were advising against travel then as well! Details of our trip are on my website:
As a first timer, the piste from Nema to Tombouctou seemed rather rough, though with hindsight pretty average; parts in Mali were graded (red) piste. The website has photos of the route as well as some GPS.
From Tombouctou to Mopti is easy. Hardtop from T to river, longish ferry, then graded piste to Goundam, then asphalt all the way to Mopti. It took us a full day in TLC.
If in Nema, take a day to visit Oualata, probably the most interesting saharan town. Also interesting mosque at Bore just after Goundam.
Enjoy your trip and don't let FCO put you off!