New Ad for Publisher's Weekly

I've been working on a little animated GIF ad for Publisher's Weekly. I'm struggling to get the file size down to an acceptable number without sacrificing the image quality too much. 

I think I'm losing the battle...

Hopefully they won't notice that I'm WAY over the limit of 40K. But at 197K, it's significantly smaller than my original 720. And that should count for something, right?