Offhand, as I recall... the RoMD boxed set was published in '93. That puts it at about the same time as the 2e FR boxed set (revised) in terms of real-time -- and that's 1367 DR.
I also remember that the RoMD boxed set references the events of Elfshadow, which was set in 1361 DR.
I can't find any direct internal sign of dating. Some of the Knights of Myth Drannor are given as a level or two higher than in the 1993 Forgotten Realms Campaign Setting, which might be an inconsistency or might indicate RoMD is set a little later than 1367.
And now that I've looked at the Campaign Guide itself, I've just noticed the Knights levels as well.
Regardless, given the publishing date in real-time, I'd still say 1367 DR is a good place to start for the actual dating of the boxed set. Ed will likely be able to specify completely where he feels it should be.