They could, although rubber has only limited usefulness without vulcanization or some other curing method. The Mesoamericans cured rubber with the juice of another naive plant; would there be anything suitable that West Africans could use?
If rubber harvesting does catch on, it would happen in the Lower Niger and Congo rather than *Mali. It would also, unfortunately, cement a slave society in those regions; one constant about wild-rubber harvesting is that it's nasty labor that few would do voluntarily for pre-industrial wages.
Hmmm. This process would be well under way by the time a book-religion gets started; writing and centralization would be ~1500 years old by then, and syncretization of village deities might have progressed somewhat like ancient Egypt. The book-religion will, as you say, add a new layer and also increase the drive for systematization. India and China might be good analogues; another person off-list has suggested Buddhism in Japan as a model.
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Anyway, a few more stray thoughts about the *Malian calendar and agriculture (which in any ancient society are closely intertwined): I doubt that the solstices and equinoxes will be very important to the *Malian year - the difference between the longest and shortest days at that latitude is only about an hour and 20 minutes, and crops depend on flood cycles rather than temperature cycles. Instead, the new year is likely to be celebrated in September when the floods begin, followed by a planting festival in October and a rice-harvest festival in February.
Between February and September, there's time for another growing season, but there probably isn't enough floodwater left for a second rice crop or anything else water-intensive. Maybe they'd learn to cultivate bambara beans as an intercrop - it's a relatively low-water crop that could be planted in April using reserved water from the rice paddies, eked out with the summer rains, and harvested in August before the next flood. Legumes are also good for nitrogen-fixing, so the beans could replenish the soil for the next rice crop, with the silt laid down by the annual floods also ensuring continued fertility. They'd have to breed a variety more tolerant of wet soils if they want to grow these beans in fallow rice paddies, but this seems like a manageable task compared to what the Mesoamericans did with maize.
The areas further from the river, where floodwaters aren't as high and irrigation is harder, are where they'd grow millet and yams. Vegetables could be grown as secondary crops in both zones, and date palms and fruit trees on the high ground. I'd guess that, based on the 3900-3700 date I set earlier for rice domestication, the full crop package would exist by the early third millennium (3000-2700), supplemented by sheep and goat's milk, microlivestock, and later by fish and waterfowl culture in the rice paddies.
Okay, I'm really interested to see how they'll be doing a few centuries down the line then. I suppose this culture will have at least a few similarities to East Asian political culture with a highly centralized government. Have cows or horses reached the Niger River region yet and if so, will there be any sleeping sickness resistant breeds down the line?
Man, your worldbuilding is excellent! How do you do it?