My touchscreen that I've attached directly to the Pi shows a black screen with a blinking cursor on boot up. However, if I attach a mini-HDMI to DVI cable to the Pi while it is off and then boot it on, it proceeds to the desktop as desired.
The monitor the DVI side is connected to does not have to be powered for this to work, but the cable must be connected to it. The cable can be removed after boot and nothing happens, though it must be reinserted if rebooted. When the Pi is booted up with the cable connected and the monitor powered, the boot screen shows first on the touchscreen, then moves to the external monitor.
I've searched the wiki and the boot issues sticky and found unsatisfactory answers. I will reflash my SD card as a last measure, but I feel like there is a simpler solution given that it works under certain conditions.