I haven’t worked on both series at the same time, but I don’t see that it would be a problem. I see it in much the same way as when you move from workplace to home to church to public space—you display different aspects of your personality. When I move from contemporary times to the past I switch attitudes and mores to match the setting.
I perused news accounts of the death of Paul Bern. I was able to get hold of some court transcripts. I found late-life memoirs of people involved with Harlow, Bern, and MGM. I read the gossip sheets from the era. The material was fascinating and contradictory. Bit by bit a pattern emerged (to my eye, at least) of Hollywood studio cover-ups of crimes by stars and producers. The police and city officials were complicit in these cover-ups. From all this data I drew my own (reasonable, I think) conclusions about Bern’s death.
I asked permission first to name characters after these fellow authors, and told them briefly what kind of character each would be. Once I had written a substantial passage that included them I sent it to them to vet. If either had been offended or homicidal about her portrayal I would change the character name to Jackie Vick.