in all of your Luminant materials (the Softbox textures) go to the Illumination tab and check GI Area Light. Do not use Irradiance Cache (Legacy) use Irradiance Cache - I see pretty good results with your file if I set it to Interior High - turn Gamma up to 1.8 to match your brightness and Samples to High.
Check the manual - C4D Prime/Render Menu/Edit Render Settings/Global Illumination/Tips and Tricks at the bottom is stuff on animation. The first words on GI and Animation are "GI and animations are technically challenging. If a single image takes a long time to render using GI, then rendering an animation with a series of these images will require very long render times. In addition, Irradiance Cache tends to flicker if its settings are set too low."... they do have good hints about things that help.