I think it interesting that Rand doesn't consider the obvious - inverted wards to sense a male channeling are probably erected all over the palace and the surrounding grounds - she may have well had an alert as soon as he used the access key. Even more obvious would be a humongous light boiling in the air in a forest not quote out of sight of the palace. She may have very well used her Compulsion, sent the nobleman back in a hurry while gathering her angreal, useful servants and etc, and then seeing the bar of white light forming, Travelled away from the area immediately. Bel'al himself realized what Moiraine was weaving based on the reaction in the air before her, and she was handling a far weaker amount of saidar to generate it compared to what Rand held. Plus, the palace itself, not being a fortress, probably has many more vantage points to see from. Heck, Moriding could have woven a gateway, informed her that the Dragon was on her doorstep and that could have been why her Compulsion on the nobleman was so thick.

Also, I think she killed Asmodean - thought so for years and even if she is now dead, that doesn't remove her from the list of suspects.