Based on my experience making the same transition, but not having any shower doors as you describe, can say that if you want to get rid of that 25-year-old grunge, baking soda, patience and elbow grease will totally do the job. By means of proof of concept, I've been using baking soda for my glass top stove for a couple of years now, and by golly, it gets even that burned-on stuff off with patience and elbow grease
Also use it to swab the decks of my old-old-old, oil-soaked wood floors, though I don't think I'd recommend it if you have good hardwood floors. Every now and again I add vinegar to the mix in order to remove more of that oil.
Have yet to use it to clean the toilet or kitchen sink, but thanks for the inspiration. Difficult to give up the Comet I've always used, but by golly, I'm gonna try.