With my success burrowing between the layers of glass that make up the oven door yesterday, tonight I set to clean the true grimy inside-facing glass.
I wanted to avoid noxious chemicals, so I opted for baking soda and vinegar plus elbow grease. It worked!
I made a paste of baking soda and water, brushed it on the open oven door, sprayed on household vinegar, waited 15 minutes, and then scrubbed and scraped. The seemingly impenetrable was penetrated and the result, if not brand-new-looking, is certainly an oven door transformed.