Well, that's frustrating. But, I have had that problem before as well. What I did, depending on how much more room you need, is I took a spade bit the size of my snap and drilled out the depth I needed. If you have a french skive you can do much the same thing.
Basically the idea is to cut away a circle of leather just wide enough that your snap sets lower than it would.
And, if you are worried about the line coming up, stitch around the snap.
Unfortunately 7/16 I think is as long as they get. You could try and separate the layers and set the snap between the layers as well. But you wouldn't be able to use the cap part, just the flat base post for both sides of the snap.
Anywho, hope my experience with your frustration helps a bit