Working in conjunction with Henry Winkler at Monument Pictures, Birnbaum produced the well-received "Young Sherlock Holmes" and "The Sure Thing" (both 1985). In his brief stints as president of the Guber/Peters Company (c. 1985-87) and later United Artists (c. 1987-88), his efforts helped realize a series of respected and generally popular productions including Barry Levinson's Oscar-winning "Rain Man", "I'm Gonna Git You Sucka" and "Gorillas in the Mist" (all 1988) and Tim Burton's "Batman" (1989). Joining Fox in 1988, Birnbaum established an amicable working relationship with chairman Joe Roth which led to a 1991 promotion increasing his interaction with marketing, video and international affairs.
In 1993, Roth left Fox to form Caravan Pictures, an independent producing company headquartered at Disney. Birnbaum was a salaried producer until Roth became chairman of Disney in 1993, when Birnbaum became Caravan's head. Caravan's first release was the indifferently-received remake of "The Three Musketeers" (1993), but the company has remained active, turning out films ranging from the Sandra Bullock vehicle "While You Were Sleeping" and "Powder" (both 1995) and the Fran Drescher comedy "The Beautician and the Beast" (1997). Other 'Caravans' have included "Angels in the Outfield" (1994), Jeremiah Chechik's "Tall Tale: The Unbelievable Adventures of Pecos Bill" (1995), "Celtic Pride" (1996) the unsuccessful Eddie Murphy action comedy, "Metro" and the John Cusack vehicle "Grosse Point Blank" (both 1997). Also that year, Birnbaum produced the kid comedy "Rocket Man" and Ridley Scott's "In Pursuit of Honor", with Demi Moore as an army recruit.
Birnbaum also worked in TV, beginning with Henry Winkler's Fair Dinkum Productions, which produced the medical series "Ryan's Four" (ABC, 1983), the TV- movie "When Your Lover Leaves" (NBC, 1983), the teen drinking cautionary tale "All the Kids Do It" (CBS, 1984), the PBS "Wonderworks" special "Happily Ever After" (PBS, 1985) and "Scandal Sheet" (ABC, 1985). With Guber/Peters, Birnbaum co- produced the thriller "Bay Coven" (NBC, 1987), thereafter abandoning TV for his film career. He was seen on the small screen, however, as an interviewee on "Naked Hollywood" (A&E, 1991).