The elite phone number or lounge agents are always the best bet. Like others, I've called from a plane with concern about making a connection, they've held me a seat on a later flight just in case with no issue. I've sometimes made the earlier lfight and sometimes not but they have always helped me, rebooked multiple times if needed and worked miracles when possible. Sometimes they just cant get me out past the tornado (in April in Chicago but they sure as heck tried) but that is to be expected.
I'm EXP now but have had great luck even before that
I've never done well with chat (figure it is just me) but have had great luck with the Twitter team for non-emergency situations