People moves, but cities and their ruins generally don't. We know where Niani was, and we know it was Mali's capital. No amount of population movement can explain that away.
Mandé being the majority of Mali doesn't help your case, because the majority of the population in Mali doesn't live in the freaking Sahara. They live in the south-western part of the country, the region closest to Guinea, and also the region that's better known as "nowhere near the Sahara".
Reference:
http://sedac.ciesin.org/downloads/maps/grump-v1/grump-v1-population-density/mlidens.jpg population density in Mali. Note how the largest population densities are in the south-west corner (aka, "Not the Sahara").
Reference 2 :
http://www.fao.org/ag/agp/agpc/doc/counprof/Mali/vegmap.jpg (The dotted part is outright deserting ; dark orange is dry steppe so fairly desertic ; medium orange is shrub steppes (not really that desertic), pale yellow is grassland steppes (not desertic at all), pale green is savanna (lush grass and trees), and dark green is forested savanna (as above with more trees). Purple is the Niger flood plain.
Note how the population map in reference 1 put pretty much all the population in the grassland steppes and savanna regions.
Reference 3:
http://www.fao.org/ag/agp/agpc/doc/counprof/Mali/ethnicmap.htm The mande people in Mali are in olive green - bambara in vertical slice, and the mandinka (the actual founders of the Empire of Mali) in green dots. Note that they are on the Southwest border, right next to Guinea.
Contrast with map 1 (they're in the corner with the most population density) and map 2 (they live in the savannah region, which, once again, at the risk of repeating myself, is
not the freaking Sahara.
So, given that.
1)We know, in fact, where the Mandinka and Mande people live today.
2)We know where the capitals of Mali were located (Niani, ruins found, and Kangaba, village of that name remain in that area to this day).
3)We know where the remnants of the Mali empire were located after it collapsed (from the contemporary Tarikh al-Sudan, composed at the time when those remnants would have still existed, so an actual written account of the situation at the time).
And that 1, 2 and 3
all point to the same region around the Mali-Guinea border, we can, with a high degree of certainty, state that the heartland of the freaking Mali Empire was, in fact, the savannah/forest region on the Guinea-Mali border, otherwise known as
not the Sahara.
Whether you like it or not.