Here's how I can see the film. Either as starting from square one where Bill Murray is Bruce Wayne and Eddie Murphy is Robin, and maybe make Eddie Murphy into the role as butler as well to give him more of a reason to be Robin, a comic relief potential of the downtrodden guy who has to follow his boss on his whacky stuff, and to play on 80s race discussion comedy. Or, to either have him be the son or nephew of Bruce Wayne, who has potentially died and left him this mansion or who could still be alive, and Murray discovers the Batman stuff and becomes Batman, and then Murray takes on the mantle of Batman with Eddie Murphy as his friend or butler or whatever becoming Robin. Murphy could be either a preexisting friend, or he could be like a criminial or an average guy who Murray takes under his wing and makes his friend. In that latter case, Murray could just play some schlub who either Bruce Wayne takes under his wing or who stumbles across Batman stuff or for whatever reason decides to become the Batman.
In whatever case, I would see Adam West and Burt Ward doing some cameo or cameo role with at least one "this looks familiar" moment. West could be Batman in a film that links up with the original series or is a separate thing but still decides to cast West as Batman, or he could play Commissioner Gordon, or he could just make a brief cameo.
In whatever case, I feel an 80s Batman comedy would be like Trading Places or Ghosbusters or any of those comedies similar to those in tone, rather than some whacky attempt at camp. There may be a brief homage moment to campiness, but I do not believe had this film happened, camp would have been the tone. On a similar note, I could see a number of homages to the 60s show laced throughout the film. I could also see that "f**k the original fans" trope of something from the 60s show or Batman in general being brought up which is true to either the Batman show or the comics, and then the characters being "oh, that's silly/stupid".