I hesitate to release this information because it is from my Mom. She makes cicken & dumplins that are always fought over at church dinners and family reunions. The funny thing is that the dough is simpler than any other recipe that I have ever seen.
The dough is a simple mixture of canned Cream of Chicken soup and enough self rising flour to make a sticky but workable dough. Thats it. I am very familiar with the texture that you describe, and trust me. This will accomplish that with a ton of awesome flavor to boot. Two cups of flour per can is what I always start with. If it needs more I add it.
I promise you will not regret this if you try it.