EXCLUSIVE: In its first go picture, Limelight has set an April start date for Palm Springs, a Max Barbakow-directed comedy that will star Andy Samberg, Cristin Milioti and J.K. Simmons. The comedy has a script by Andy Siara (Lodge 49), and it will be produced by Samberg, Akiva Schaffer, Jorma Taccone and Becky…