I always saw the One Power as infinite, so what Rand and Nyn did never made much sense to me, but I wrote it off by not thinking too much about it. But if the One Power is finite, and they actually channeled all of it over the course of the day, it would be entirely possible for them to funnel all of saidin through Shadar Logoth, leaving the taint behind, and saidin returning to the overall saidin pool normal and taint-free.

Although if looked at that way, there's still the issue that if clean saidin is added to a pool of tainted saidin, wouldn't the taint spread to it too? Maybe the taint itself would get diluted, but that would mean that no matter how much saidin they funneled through Shadar Logoth, some taint would always remain. Which seems problematic.