Don't know if you are still interested, but I did some investigation of this a couple of years back. We were dealing with a weir operating v close to modular limit, so the position of this and further drowning effects was important.
I compared formulae/charts provided by Ackers (1971); King and Brater (Villemonte) (1963); Davis (1952); Bligh (1927) and Bos (1989). The comparison showed that there are significant differences in the results obtained by these different approaches. Withough going into too much detail I found that if you are using the Villemonte equation then you are probably getting results at the conservative end of the scale (ie indicating that drowning has a greater impact on discharge, with a lower modular limit). The more recent Ackers (and Bos), on the other hand, indicates that the modular limit is at around 0.9 and flow rates decrease rapidly above this. It sounds like this is more akin to what HEC-RAS is telling you.
So, it comes down to whether you need to be conservative or are struggling to get something to work. Personally I put a lot of faith in Bos in these things, but it is aimed at flow measurement structures and so may give an optimistic view of things on other less "refined" weirs. Hope this provides some useful context.
