Have you tried pumping for a minute or two on the left to "tap off" the initial flow before you feed her? I know babies can be pretty impatient if they suddenly realize they're hungry, but if she gives you signals that her appetite is revving up, you might have time to do this.
There's also a simple, lightweight, and extremely portable hand pump that would allow you to quietly pump one-handed on the left while she starts on the right. If you catch up with the flow, you could switch her to the left side.
I had this "too much for baby" problem many years ago before pumps were widely available. I would put my daughter on the slower breast for the first few minutes and soak up the fountain from the other breast with a clean washcloth. I didn't have to work for her first year, though, so losing that milk was not a big deal. The flow always slowed down after the initial letdown.