I think I was off on my total current draw calculation. But the fact is, I am happy with the performance of the 80 LED strips when powered through 1117 regulator by 4 AAA batteries (yes, 4xAAA). These are for kites at night, so full brightness is not often necessary and I am happy with the brightness that I am getting from them and the battery endurance which results.
https://youtu.be/d98eaIsBDbw
https://youtu.be/e3CRJ5Rdoj8
So I will try your ideas with the larger cap, diode, and maybe get some of the other module. If that fails I will live with the 1117 regulator.
Cheers,
John