I find leg press to be really hard on my back, although it's hard on it in a different way. I do tend to go deeper than I should though. That makes my low back curl.
The single best exercise for quads that put not pressure on my back are single leg split squats. The amount of weight you use will humble you at first. And you will get an amazing stretch of the back quad that is supporting your balance. You will also relieve all pressure on your back. And you will discover any imbalances in hip, glute, ham and quad strength. My left glute first so much better than my right.
Seriously give them a shot. Find a sit up bench with those roller things on the end where the feet wrap under. Start with a broom stick for balance and just do them unweighted for starters. Just get used to the stretch of the back leg and the balance it takes to do them correctly. Then grab some dumbbells (no more than 45s to start with, seriously, trust me) and then eventually you can use a barbell if you need to relieve the grip.