Another update. So my 3D print came in, and I filed the PCB down even more.
Here is the final size of my PCB before it was inserted into the expansion card housing. I may have gone a bit overboard on the front corners.
And here it is in the housing.
After I confirmed that the PCB fit and the USB-C port went through the hole, I took out another expansion card so I had a reference for how far out I should let the USB-C plug stick out. Then, I put super glue on the bottom and sides of the SD PCB and set it in place on the 3D printed housing.
Here is the finished result. It’s a bit more work to get it in and out, but it’s totally doable and I’m very happy with it. It even fits in my unofficial expansion card carrying case (available here), and I now have a USB-C to SD adapter that I can use with my phone too!
One downside when using this adapter in Windows is that after ejecting it, the expansion card must be unplugged and reinserted in order for the computer to recognize an SD card from it again. This is not a problem I noticed in Linux (Pop!_OS for me). Again, thank you to everyone in this thread for your findings, this is awesome!