Suggestion for solution: interested parties taboo "rationality" and privately write a (roughly) three sentence summary of just what it is we think we're about. At a later time, interested parties post their summaries, and then try to pick out common themes and keywords to identify a unique label that doesn't have the name collision problem identified in the OP.
And then, about three minutes later, we'd have to taboo said common keywords and then write a three sentence summary of said keyword and present it to each other in order to pick out common themes and keywords, and repeat this process over and over...and not being able to actually talk about what we were supposed to talk about.
Can't we just argue over what is being done in the name of rationality, rather than arguing over the word "rationality" itself?
You see, I've seen the word "rationalism" used to mean all five of these things at different times:
Edited to reinstate that proposed solution, since this discussion is presumably finished.