After digging in the graphics drivers fail INF file for a bit, I found an exact match for my device ID but also found what looked like a windows build version requirement in this line
[IntelGfx.NTamd64.10.0...16225]
I’m not sure about the syntax but this kind of reads like a requirement that windows be (at least?) version 10.0 build 16225. My windows version was much older than that, at 10.0.10586 Build 10586 (which came out in 2015). So I decided to try and get windows to update.
Windows update insisted that the system was up to date. So I downloaded and used windows 10 update assistant, which took several hours to go through the process, but worked like a charm. When it finally completed, everything on the laptop, including the external HDMI monitor connection, worked perfectly.