Removing Excess Material for Deep Cuts

I will try to make this as comprehendible as possible.

I am using V-Carve and imported a 3D file (Marine Corps Eagle, Globe & Anchor). I can remove excess material over the area that will be carved out to speed up the process. My issue comes when it goes to the deep edge cuts. If the material is thicker than the bit is long or using a 1/16th bit where the flutes are 1/4" long and then it transitions to 1/8"; is there a way to remove the material outside the area I am looking to cut?

You could create a pocket outside your design to bring the thickness down. Why not just use a larger end mill?
Can you share the project or a picture, so we get a better idea of the issue?