I stopped by the local autoparts store and purchased a tube of multi-purpose wheel bearing grease. Now all I had to do was rebuild the spring barrel. Here is how it went:
First was the dirty job of cleaning. I recommend taking pictures as you go along so that you have a reference to look at during reassembly. To remove the spring I took a hold of the center and eased it out. The first half goes calmly and then it jumped out. Being careful not to damage the tail hole in the spring, I separated the spring from the barrel. I used mineral spirits to clean all the parts (and several rags).
Once all the parts (and my hands) were clean, I greased the inside of the barrel. Before attempting to reinstall the main spring, I reshaped the ends of the spring. The outermost end that hooks in the barrel needed to have a slight bend to allow for the hole to nest tightly around the post in the barrel. The inner most end had to have the curl made smaller so that it held the center winding post tightly. I didn't want to have to open the barrel again because one of the spring ends had come loose. After reviewing pictures I had taken and was sure that I knew which way the spring needed to be wound, I hooked the end of the spring onto the barrel post and wond the spring back into the barrel.
As recommended, I added the multi-purpose wheel bearing grease to the center of the barrel...and then a little on the edges of the spring. Again cleaning the hands.
Last thing to do was to reassemble the spring barrel. There is a felt pad that is between the outer cover and the spring retention plate. I lubricated this with a soaking of 30 weight motor oil. Carefully I bent the three tabs to hold the assembly together and gave the assembly one last wipe-down and cleaned my hands again.
This brings me back to where I was on the Amberola 30 restoration. Thank you for all the advice, direction, and wise counsel. Today I will reinstall the mainspring, winding assembly, and get back to testing.