Why in the world do you assume that the end of the Breaking was an exact date, and the reinvention of channeling began only then?

The way it probably worked was, in the first 150-200 years of the Breaking (which itself officially started several decades after LTT's mission, remember. Latra Pose had time to round up other Foresaken and become a famous woman before enough men started going mad to start the Breaking proper), the AoL advanced knowledge was gradually eroded. More and more women received half-baked training at some basic weaves for survival, and special skills were ignored. Women probably got enough training so they won't kill themselves, then sent off (at which point they would be unlikely to be strong enough for Traveling). By the time the Breaking is done, all that survives is very basic knowledge.

By 98 AB, groups have formed, several with very non-overlapping skill-sets.

The entire knowledge base of the Tower at its founding was definitely NOT equal to its current extent. For one thing, several Earth and Fire intensive weaves likely were widely used then that were slowly ignored as women strong in Earth and Fire became rarer. But many weaves were also absent.

We know that there was a great deal of research since the Tower's founding and up to the Trolloc Wars, at least. Tons of ter'angreal were found and their functions determined. For 300 years, research was done on alternate ways to fight the taint than simply gentle men. Research was done into linked circles (and a non-AoL way was even found to make a forced circle, that was then lost), and so on. Nothing indicates that a lot of current Tower knowledge didn't come from those times. That, in fact, is far more likely than the Tower having a continuous knowledge base from the AoL, just one that shrank a lot.