Thought I'd take a minute and give a final report on this project.
The initial ammonia treatment and subsequent pressure washing did end up yielding some unexpected benefits. After that portion of the cleaning I had left the center section and lid out overnight to dry (like that was going to be a problem here in the Land of Where the Temperature Doesn't Drop Below 90°F At Night). On Sunday morning I went out to begin a scraping and oven cleaner session and discovered that much of the material on the inside of the two pieces had dried and cracked so I was able to scrap off about 90% of all the stuff before breaking out the oven cleaner. In reality, with one good spraying with oven cleaner and about 30 minutes of saturation time I was able to get both pieces very clean. I followed that up with a pass of dish soap and water followed by another thorough rinse with the pressure washer.
I know that it is very unusual to do a deep cleaning on a WSM but I had my reasons. Just thought I share the experience so that anyone else who needs to go down this road can learn from my process.
Here endeth the insanity!