"I ground the back flat as a pancake."
Now that concerns me! Why did you do that?
Pat's bow was Osage, and quite oily. TB3 won't adhere well to oily woods IMO. He'd used a varnished barrier between the wood and sinew and only had one spot that lifted. Your bow being hickory, is a totally different situation.
You're going to need at a minimum, two layers, and perhaps a third. Trick is to use the least amount of sinew/glue to get the job done without adding a bunch of excess weight. Here's what I do:
Do first layer limb width. Stairstep in for second course (using about 1/3 less sinew/glue for this layer). Last course if needed, one strip/bundle (2/3 less sinew/glue for this layer) of sinew right down the middle of the limbs (good idea for bows with high crowned backs)........Art