What happened with Ramshalan seems to suggest that Aran'gar does have the necessary skill. She placed compulsion on Ramshalan with no warning and in just few minutes, and did so in a way that left Ramshalans mind intact, just manipulated. And that was with just few moments to work with.

With Egwene, Aran'gar would have had weeks or months to slowly and carefully place delicate compulsions with as much care and precision as was needed. She could even have asked for advice from Graendal on what would work best given the timeframe.

As for why she used others to sow discontent too, I would say probably because she could not use Egwene for it so easily. Remember that what we are talking about here is the idea that Aran'gar placed some very subtle compulsions in Egwenes mind that no one noticed and which will come to play in the final book.

If Aran'gar had placed a compulsion on Egwene that had her march to her followers and declare that its time to surrender to Elaida or anything utterly out of character like that, she would likely have been delved and Aran'gar discovered.