I am surprised that the glue keeps it stiff enough to act as a stabilizer. This would certainly eliminate the stop of pulling off the stabilizer. What type of glue are you using?
I used Lynette Anderson's method for making my bias stems. I used a glue stick to place them into position and heat set them. My borders were added to the completed top. I then laid it out on the floor and positioned one side at a time. Starting at one curve and ending at the other curve, using my glue stick and then ironing everything in place. It holds great. I am sewing the applique on with a 1.0 - 1.0 zigzag stitch, so my needle runs along the outside edge of the applique and just catches a few threads of the fabric when it goes in to make the zigzag stitch. I have monofilament thread in the top with Superior Bottom Line that matches my background fabric in the bobbin. Where there is a main steam, I place the leaf stem underneath the main stem. The flower I place on top of the stems. Where there was an raw edge stem I zigzaged around it with monofilament thread. The glue keeps it nice and stiff and acts as a stabilizer. It is taking me awhile to zigzag but I like the finished look. When one side is done than I will glue down another side, set the glue with the iron, and go to the sewing machine to start stitching all that down. When done, unless you look real close, it looks like it was done by hand.
Okay. Glad to hear that someone else is on the same page as I am. I do think it will look better to have a continuous stem instead of trying to piece it. I'm doing the zigzag stitch with the poly for the first time instead of hand applique and do like the look and the fact that it is very fast.