Well, to be honest, I don't really see how this applies to FreeDoom itself. It's the engines that need to worry about copyright issues, since they're the ones including the strings, not us. As long as we aren't the ones including any trademarked strings in the IWAD, I think we would be safe.
The strings contain trademarked names et al. which are not technically covered by the GPL. It's a very gray and murky area of licensing, and it'd be best to stay far away from it.
What I mean is, ignoring the engines (which this project is not a part of, it only covers the IWADs), if you were to look at any FreeDoom related content (e.g. opening the IWAD and looking inside), you will not find any references to the original stuff, so why bother? And consistency doesn't really matter either, if you load a PWAD with intention of running under the id IWAD, there's a slight chance things won't match up anyway.
If id included the strings in the free release of the source code, I don't think they care that much. The fact that the strings are in the free source code could mean that they are open to use with any IWAD. (but I'm not a lawyer, but still, I think they are not considered part of owning the full game)
Besides, what's the point anyway if some (even if not many) source ports do not include BEX support (or even DEH), and what about ports that add more strings related to the original content (like ZDoom's obituary messages). Should we really bother if we're gonna have to deal with consistency across every port?
Though one thing I do think is an issue, we are still using id's names for the difficulty levels (like Ultra-Violence, and Nightmare!, etc.). How are we in the right to be using these titles? Perhaps we should name these "Skill X" with a number in place of X. Or maybe "Very easy, easy, normal, hard, very hard"?
This is more of an issue since it actually deals with what is in the IWAD, not in the source which we have no control over anyway (as it is external and not related to this project).