I have it worse than you, I'm performing this on Thursday...
Anyway, my teacher's usual trick for this is to rely on the left hand's "inner voice". Since this is hard to put into words, take a look at this to see what I mean:
The idea is to focus on the highlighted voice's legato (not necessarily to bring it out!). It will ensure better hand stability than either other voice would. Here's some suggestions as to how to put this into practise:
1. Without pedal, starting slowly, play the inner voice as legato as possible, and the other voices non legato (not staccato). Make sure you always hit all the notes simultaneously.
2. Play the inner voice alone.
3. Play the left hand as it is written, with pedal, but while singing or thinking about the inner voice's notes.
It goes without saying that refraining from looking at the keyboard benefits these exercises greatly.
I know it may seem a bit unusual and tedious, but I can assure you that it works wonders. By the time you're comfortable with the above, your left hand will most definitely have improved significantly, and not *only* as far as speed goes. Best of luck!