Best Way to Match Lighting/Color Balance Across Multiple GIF Frames

I'm in quite the pickle. I'm editing a 53-frame animated GIF. The lighting, shadows, and color balance in each frame are all slightly different - despite efforts to color correct in Lightroom before taking this project into Photoshop. I thought using the Match Color tool for each frame would solve my problem, but it has not. It'll work for some frames but not others. Does anyone have any suggestions as to how to fix this? I really do not want to have to manually adjust each frame. See video of the issue here: https://vimeo.com/716817633/a250021372