My first thought was pick up some big rocks.
I read in an article that crouching down around big cats is seen as an act of aggression, so I guess the time to grab a rock is when it's as far away as possible.
I thought about that too. Picking up a rock would have likely led to a charge that didn't stop.
I had a similar incident with a mama black bear a few decades ago. I was backpacking by myself in Sequoia and there were tons of bears out at that time. Rocks and shouting scared them all off as they usually do. Except for one. I saw a bear sitting maybe 30' off the trail and it wouldn't go no matter what I did. I (maybe stupidly) decided to just continue on figuring the bear would sit there. It (she) didn't. She charged me and you've never seen a guy run backwards so fast in your life. She stopped after maybe 50' and just started doing aggressive display at that point. Which was also the point where I finally caught that at the opposite side of the trail, up in a tree, were two cubs. I had walked right between her and them.
Because of the terrain, there were no easy ways around them other than back where I was coming from. I ended up scootching my ass down a semi-cliff to the creek below, and wading for a good 1/4 mile until I found a place to climb back on to the trail.