I stopped doing the leg press a few years ago when I read an article (I think on T Nation) which had all sorts of technical stuff in it about torque and compression and basically showed that the leg press is a really crappy exercise that's horrible for the lower back.
I switched to something I call a cable walk-back. (Don't know if it has a real name.) Using only one side of a cable machine, set the handle fairly low (I use setting #11) and the handle of your choice. Drop into a squat position, extend your arms, lean back with your weight in your heels and slowly pull the weight as you walk backwards until the cable runs out. Then slowly walk it back. It's kind of like doing a controlled tug-of-war.
You'll get the work in your legs, glutes and lower back without any compression.
In the meantime, do side and forward planks throughout the day until your back recovers.