With the starch method (if it's what I've tried) you must iron the starched fabric edges over your template. This dries the starch and holds the edge in place. The problems I've had with starch are that it's easy to press unwanted pleats into your curves, and it's difficult to press tiny pieces, even if you use a little Clover iron.
Glue sticks are tacky enough to hold the fabric edges in place without ironing. And the beauty of the wash-away stabilizers is that you can glue directly to your template and not need to remove the template later.
I've made small (about 3/8") circles using the stabilizer/glue stick and a stiletto for turning the edges -- it works great! No experience with Lynette's sticks, but it might be helpful to have the second, forked stick to hold little pieces.
I don't know why Lynette switches to basting glue to hold the prepared appliques to the fabric -- I just use a little dab from the glue stick. It all washes out later -- after sewing, I soak my block in warm water for a couple hours (as recommended by Sharon Schamber) to dissolve the glue. Rinse, air dry, and press face down on a towel.
Be sure you use a WASHABLE, not a permanent, glue stick. And, BTW, you can use Elmer's Washable School Glue in place of expensive basting glue...
Looks like you could use a computer mouse pad or something similar as a rubber mat. I'm not sure about the mountain-building...someone should do an experiment!