The main purpose of lifting the heel is for people with poor ankle dorsiflexion. That way, when you do a full squat with your hamstrings meeting your calves, it doesn't require your heels to elevate off the floor causing instability.
Without seeing your form in person it's impossible to say for sure, though it sounds to me like it might be causing you to shift the weight forward, in which case you may be trying to push through your toes. Again, try to concentrate on pushing through the heels to hit that posterior chain.
Then again it could be a combination of overall lower body inflexibility - hip flexors, glutes, hamstrings, and ankles.
Just be careful squatting with weight. Lower back injuries suck bad.
Here's a good video and in depth explanation of technique: YouTube - Squat Rx #4
The first girl in this video has a beautiful technique, as well as a gorgeous posterior chain - notice that even though she squats to full depth, she never loses that lumber arch, and her feet stay flat - YouTube - Overhead Squat - Bodyweight x 15 reps
As an aside, I really dislike Crossfit though. If you watch these girls, you can see how their form suffers as they get higher in reps.