Probably is a bit late for this since you already got help, but would it work using a compressed format other than vanilla ZIP? For instance 7z or tar-bz archive? Of course, those give your players a bit of a headache uncompressing the files in the end, since they're non-standard formats.
(Another way to get around this could be zipping your zip archive in another zip archive so the main zip only contains one file, but because of how compression works, this probably will just make the download LARGER)
...oh, wait, you said browser game. Derp, then I guess it wouldn't even load properly. Sorry, should've read the question more thoroughly before trying to help. x3