"The only felt I can find in my area is thin and stiff. Are there any online sources for high-quality felt?"
You've come to the right place, Theresa—we love felt! In fact, we have an entire section of the website devoted to felt projects. As for our sources, we have several that sell high-quality wool felt.
Magic Cabin Dolls has a broad spectrum of colors.
A Child's Dream Come True has plant-dyed felt.
FilzFelt has heavyweight felt.
Purl sells wool felt in bundles, including eight different colors.