Eomer and the ladies: a discrepancy?

[Mithalwen]

It so happens that I have had cause to examine closely the Tale of years for the period between the War of the Ring and the journey home for the hobbits and I have noticed what seems to be a discepancy in comparison to the text.

In Many Partings it says of Eomer "and when they sat all at table... he beheld the beauty of the ladies that he saw and was filled with great wonder". He then sends for Gimli to confess he prefers Arwen.

However in the Tale of Years it says that Elladan and Elrohir brought Arwen to Edoras on June 14 and didn't leave for Gondor til the 16th.

Until now I had always assumed that Eomer saw Arwen and Galadriel for the first time on the occasion cited above and even now, I think that is the implication of the passage in isolation.

However I find it hard to believe that no matter how busy Eomer was in the aftermath of the war that he would not have received such important guests personally, especially since Elladan and Elrohir had travelled with the Rohirrim.

I can devise explanations of course but none to my satisfaction. The ladies may have been veiled but this does not seem particularly likely culturally for elves. Anywhere else in the Mark where Eomermay have had urgent business is either on the route or close enough that not to greet the escort would seem grossly discourteous.

Can anyone explain this or am I reading this wrongly?