Hi Wolfgang and Michael,
Thank you for your quick responses and help.
Regarding your (Michael) question about clarification, I have a total of 51 comparisons. The individual testing of moderators is done on all studies for which that moderator is available. The model with all moderators is indeed a subset of these 51 studies (k=27), as for each moderator, different studies are excluded because of missing values.
When I first brought this issue up in this mailing list a few months ago, Wolfgang suggested a side-by-side comparison of the moderator tests, so that I present both the individual moderator tests, as well as the results when all moderators are included in the same model. I think this makes sense, but I want to make sure I interpret/present these findings correctly (which, it seems, I am not doing so far).