I realize this update was long time in coming, but here goes.
The goal of removal is to get to finished natural woodwork, so painting was never on the table.
In the end, I got multiple bids on different parts of the job. I'm starting with half of my house. I hired out one quarter and I am working hard on the other quarter. I chose which quarter to hire out based on how many layers of lead paint I thought there were (using my home lead test kits).
I haven't died yet, so I suppose I am not messing anything up too badly. My method is to use a chemical stripper (Soygel), then a high quality scraper, then a couple different grades of sandpaper + dental picks for detail work. It is slow, slow going. Luckily, I am really stubborn.
To deal with the lead, I chose a stripper that supposedly helps encapsulate the lead dust. I vacuum up scrapings right away with a good vacuum dedicated to this project. I wear a lead paint-specific mask. And I also will sometimes wipe down the wood with a barely damp rag, because my reading says that this helps prevent getting the dust into the air in the first place.
Given the price of the contract on half of the work, I am glad I am tackling some of it myself. But this is a really, really big project that will likely be going on for many years to come.