Steve,
Whenever I'm doing applique that will require me to snip the turn-under allowance closer that 3/16" I trim as I go. I only trim about an inch at a time and once I've got that nearly turned, I trim another inch, and so on. You can trim to your normal ¼" to begin with, or even larger, and then trim to the tinier allowance later, as you work it.
I saw her soft edge applique on Simply Quilts many years ago. She's really come up with some incredible ideas in her quilting career.