In the course of providing an answer to Did the Japanese Spider-Man ever have a TV crossover with any other Super Sentai characters?, I found that there was a stage show which involved the "Japanese Spider-Man" crossing over with Battle Fever J (as well as with Kamen Rider, Ultraman, and Doraemon), Battle Fever J Stage Show at 3 Heroes Korakuen Yuenchi. Unfortunately, there doesn't seem to be a ton of information about it, other than this promotional photo showing the actors posing together.
The newest character depicted in this image is Ultraman Joneus, who debuted in 1980 (or maybe 1979 as per the comment below). A selection of commercials between 1983 and 1994 for the Korakuen amusement park show a number of bits from the stage shows, but I don't see anything with Battle Fever J (although I do see some of the other Kamen Riders and at one point, a poster with a cartoon representation of Doraemon pops up). That suggests this probably ran in some period between 1980 to 1983 (because I doubt they would've had a later show featuring characters that were cutting edge a decade earlier).
So, when did this stage show take place?