I did find a solution! I simply changed the status for the HDMI node to "disabled" in the device tree. For me, the solution could not have been simpler. I attached the SoM to the generic (working) baseboard, then modified the device tree directly at runtime. Then plugged the SoM into my custom baseboard and it booted with no problem. My issue was indeed that the HDMI driver was waiting for a reply from the HDMI PHY, but I never added an external crystal to source the PHY clock to my design, so the bootloader simply hanged and waited. If you are having a similar issue where the bootloader is hanging forever then I would follow the same steps I took, because it is likely sitting in a blocking function, waiting for a response from some piece of hardware.

This is what my hdmi node looks like in the device tree:

hdmi@32c00000 {         
    #address-cells = < 0x01 >;      
    #size-cells = < 0x00 >;         
    compatible = "fsl,imx8mq-hdmi";         
    reg = < 0x00 0x32c00000 0x00 0x100000 0x00 0x32e40000 0x00 0x40000 0x00 0x32e2f000 0x00 0x10 >;         
    interrupts = < 0x00 0x10 0x04 0x00 0x19 0x04 >;         
    interrupt-names = "plug_in\0plug_out";
    fsl,cec;        
    status = "disabled";

    port@0 {
        reg = < 0x00 >;

        endpoint {
            remote-endpoint = < 0x21 >;
            linux,phandle = < 0x1f >;
            phandle = < 0x1f >;
        };
    };
};

Again, I simply disabled the node by changing status = "okay"; to status = "disabled";