Setting a longer Re-Enumeration timeout has no effect, however I do think I've found the problem and it's the design on our end.
What's happening is our design is a USB-C sink, and when we enter the bootloader, the USB-C_CTRL0 and USB-C_CTRL1 pins are not turning on the FETs that provides input (USB-C_PWR) to a 12V regulator that powers other electronics onboard. One of the parts that is powered by this regulator is a USB 2.0 mux, which points the USB 2.0 to either the CYPD3120 (for configuration/billboard/bootloading) or a PSoC5LP for other operations.
When we enter the bootloader, the FETs are turned off, the mux never receives power, so the EZPD Configuration Utility can't find the Bootloader HID interface.
We are going to address the problem in the next prototype of the design to make the USB2.0 mux dependent on VBUS rather than USB-C_PWR, and that should allow us to connect to the USB HID Bootloader interface when VBUS_C_CTRL0 and VBUS_C_CTRL1 haven't yet been set.