I do quilt as you go and haven't found the result to be too stiff. It may depend on the batting and the strip fabric.
I use this tutorial:
http://welshquilter.blogspot.com/200...as-you-go.html with the adjustment of a change in the narrow strip to be 1 and 1/8" instead of 1".
Doing QAYG makes the whole quilting thing manageable for me, and I love it!
Dayle
P.S. My avatar is QAYG