So here's a first draft of what I'm thinking for the Taic languages. As in the maps previous people have posted, red indicates the rough area of the Taic urheimat ca. 10,000 BK, yellow represents expansion by 6,000 BK, and green represents expansion by 2,000 BK.
The basic concept here is that the language family initially expands along the major rivers in the immediate area, practicing relatively simple agriculture. By 6,000 BK the language family has broken up into two groups of daughters, the "High Taic" languages in the more mountainous east and the "Low Taic" languages in the flatter west. In both regions population pressures lead to social change, but the direction of that change depends on the terrain.
On the fertile floodplains of the west, the Low Taic speaking peoples begin to aggregate into larger, fortified settlements, the most successful of which eventually grow into true cities. They expand their territory somewhat over the centuries, but increasing conflict with agriculturalized neighbors means that their expansion is mostly demographic rather than geographical.
In the east, a more radical change takes place, as a series of innovation in agriculture (including new and hardier crop strains, the development of terrace agriculture, and the transition to a more mixed agricultural model relying more heavily on animal husbandry) allows the High Leic speakers to expand into the more marginal, mountainous regions surrounding the river valley. Their settlements are smaller than those in the west, at least initially, but their unique cultural adaptations to the highlands allow them to spread over a large territory relatively rapidly.
Let me know what you think! it's all a little rough right now, so constructive criticism is appreciated. Incidentally, I suspect that Loglorn's people won't have too much difficulty dominating the Taic-speaking coastlands when they arrive, as even the Low Taic peoples are likely relatively backwards in terms of nautical technology.