A couple things I notice... the comment about "I've never done anything that complicated in my life"... I just went through mine, also my first lathe, and though not complicated, there are a lot of little parts on this guy, and while the parts manual is a great help, it's no step by step shop manual. Go slow, take lots of pictures. If you've ever rebuilt a carburetor you'll be fine.
The second is that one of your missing handles is in your back gear- that lever is actually from your compound wheel not lost.
As much as you may be lusting to get into that headstock, I'd start with all the other parts fist to get yourself accustomed to the type of 1930's engineering you'll be encountering- go through your tailstock first, then clean and rebuild the compound, then dive into the headstock, paying special attention the three spring loaded detent balls you don't want to lose- one is between the headstock casting and the round disk which holds the back gear lever, one is in the larger gear on engagement pin (not an issue until after you have removed the gear for cleaning and are disassembling it) and the third is in the casting of the headstock itself under the indexing pin. When you tap the indexing pin out to clean it, just be aware there is a spring loaded ball under there.