Thanks, maybe when I have time I'll try it for academic's sake.

I did what I want with this in the shell:

curl -s -o /dev/null -b $cookiejar -c $cookiejar -d $login_data $site_url 2> /dev/null
curl -s -b $cookiejar -c $cookiejar $site_url/page_i_want

way simpler. You could use shell_exec() if you want to wrap it in PHP for some reason.