Answering my own question in case it helps anyone. It turns out the ribbon for the screen (the last one removed in Step 14) wasn't far enough in the connector. I was trying it with the line about even with the "39" on the board, which wasn't far enough. After the eBay seller kindly gave me some tips, I was able to manhandle the ribbon closer to the connector, and now the screen works great!

I followed this guide, but the screen is still on the "Amazon Kindle" screen that was on the replacement when it came in the mail. I opened it to ensure the ribbons are all in place. It's fully charged (green light) and the computer can see it as a hard drive. Calibre can also see all the books are still in place. Any ideas what connection I need to recheck to get the replacement screen working? I'd love to get my old Kindle 2 back in business!