Aside from the obvious humor of the situation, there is only really the one reason to think it even approaching "likely" ... Aran'gar's comments an disguising herself as another FS (which btw I agree with you on).

However, there are a few small things here...

Aran'gar has a fluid enough job in the rebel camp to make it easy to slip in and out without causing much fuss. And since it looks like Taim works pretty openly as a DF in the BT it wouldn't be too tough for him to be gone for long stretches at a time.

Where have we seen that Taim is stronger than Aran'gar? As far as I can tell we've never seen them together. Taim isn't as strong as Rand as early as LoC, and we've never had a comparison to Arang'gar with any of the males. But the BWB implies that he actually had great OP strength, but was undisciplined.

I don't know that it's impossible for Ishy/Moridin to also be Taim, but I tend to agree with you that it's more likely he's a 3rd ager who spent a good deal of time with Ishamael prior to the events of the books.