I'd prefer:

We invited the strippers, JFK and Stalin, to the party [two strippers, named JFK and Stalin]

if the goal is to minimize ambiguity.

I can see it being tiresome to read text where the author is continuously interjecting clarification with brackets.

The square-bracket clarifications here are meta-text designed to absolutely clarify the intended reading of the preceding text, so that the reader can contrast their understanding with the intended one.

There is no suggestion that one would do this in "regular" text.