I think a lot of people thought you were talking about for hunting leopard instead of following up after wounded.

Following your idea for following up I doubt you would need anything close to a 577. It seems to me it would be more valuable to have a faster recovery after the first shot. Maybe a 375 flanged or 500/416. At the very most a 470-500 NE if you just want more lead. From everything I have heard cats are very susceptible to shock so it seems a higher velocity 500/416 would be better for this then the 577 and the recovery would be faster.

Also I read one of Capsticks articles that said 00 buck was inefficient because of the size of the shot. Imagine a trashcan, you can get much more weight into it using balls the size of a golfball versus the size of a basketball (assuming equal density). Therefore you can get much more shot by weight into a shell if you use smaller shot. I think he suggested #1 but if you are interested I could check to be sure.