Not familiar with glass or NC studio, but use a waterjet alot at work. We have a Flow and I know that with the software we have, we an adjust the lead in and lead out cuts. Specifying a longer lead cut would help, if the lead is at a 90 degree angle to you cut path. Basically anyything you can do to get the pierce away from the part when it happens. Move the pierce from the corner of the part to an edge for more support. It really suprises me that you can't specify this.
Also, we have the ability to select what type of material we are cutting in the software. I ssume that you can do the same. If so, make sure you have the correct one selected, as this will make a big differrence.
Perhaps with a bit more info, I could help more? Just not that familiar with cutting glass as I said before. Willing to try if I can be of assistance though.