Even though the Hummingboard does not use an external PCIe clock, it seems that this issue isn't a clocking problem.
After discussing this issue with SolidRun, they suggested testing the VMX-200 PCIe video card with the PCIe driver in latest Linux 4.4 kernel. Sure enough, the card initializes correctly with the 4.4 PCIe driver.
Although the PCIe support seems much improved in the 4.4 kernel, much of the iMX6 support for the Vivante GPU, IPU, and VPU is missing in the 4.4 kernel. I located an iMX6 kernel at https://github.com/patrykk/linux-udoo.git, however I haven't had much luck getting the 5.0.11.p7.1-hfp imx-gpu-viv OpenGL libraries working with this kernel.
Does Freescale have any plans to release updates for the 4.4 LTS kernel or to backport a more reliable PCIe driver back to the 3.14 kernel? Are there updated Vivante OpenGL drivers which can run with a 4.4 kernel?