If the car is trying to roll with all four brakes on it would makes sense that only the fronts being on won't hold it either.
Once the tires are spinning the line lock should hold it though, and if your tires are in a water box they should spin pretty easy anyway.
I can't imagine your car can't light the tires right off, so maybe you are easing into the throttle too much instead of just nailing it a bit harder to break them loose more suddenly so it doesn't get a chance to push through the brakes.
Also, I don't know about your state but here in AZ a line lock on the street MUST activate your brake lights.
If this applies to you hit me up about a real easy way to do that without having to cut into brake lines to install a pressure switch.
