I've just learned that the cross-arm style is called 'California style' and that I shouldn't be doing them.
Personally, I just cannot do the clean grip style (even though I'm fine at overhead press) and find the cross-arm style comfortable and safe.
It took me forever to get my front squat technique right. I used the Stingray for a while, but in the end it was just practice and experimentation, and it's now one of my favourite exercises.
For me, the biggest challenge is to stop the feeling that the bar is going to fall off forwards at any moment. Two things to help with this:
1) As Swede says, get the bar back as far as you can towards your throat (though noting Josh's cautionary note). As you raise your elbows, your front delts make a little (or big!) hillock. The bar needs to sit in the groove between this and your clavicles, not on top of your front delt.
2) Focus on keeping your elbows high throughout the movement. When the movement gets tough, the elbows tend to sag (at least they do in the cross-arm position) and then the bar starts popping out of that nice groove you created in (1).
A narrower diameter bar, like a deadlift bar, really helped me keep the bar in the right place, and chalk can work wonders too.
Good flexibility can help - I found a raised heel helps too.
This is how I do 'em. I broke out my leotard and knee sleeves for the lift below - not perfect by any means - technique is breaking down a bit - but gives you an idea:
In this one you can just about see the set up - I get the bar as close to me as possible.