I think hand quilting the black will be very difficult because of the layers of interfacing. Make a sample using leftover interfacing to test.
If your machine has the type of foot control that allows you to make a stitch at a time (my Bernina 1230 allows me to tap the foot to raise or lower the needle, so technically is probably a half-stitch at a time), then I think it would be fairly easy to use the machine. I would either use a heavier weight black top thread (maybe 28wt ?) or double up regular thread and go very, very slowly with the machine. Experiment with different feet to see what helps you stay in the ditch the most. I have doubled regular thread simply by placing 2 spools on the machine and treating the two threads as one. Works well for me, although I think a single heavier weight thread would be preferable. I do invisible machine applique and sometimes will sew just a stitch at a time to make sure the needle placement is exactly where I want it. For me with my bad hands, this still beats hand sewing every time!