Very good point on the RPi ver 2. I’m using a RPi B+ model with BCM2835 SOC ARM v11 700Mhz CPU. This will run the Linux distributions that have the ARMv6 kernel support (such as in the base image indicated in the OSPi manual link). The RPi ver 2 model uses a Cortex-A5 CPU running at an improved 800MHz. This one requires the ARMv7 kernel to run. The Raspian image from the RPi website has been modified to include the new kernel. I believe it will also be backwards compatible with the older RPi models. Unfortunately the AMRv6 kernel is not forward compatible.
Seems to be a case of loading the new Raspian as Sean suggests. You can then layer on the needed software components for the OSPi. A second approach would be to do a little surgery to the current image on your SD card and inject the ARMv7 kernel image and modify the bootloader file. This would be non-trivial. And I guess a third approach would be to find a RPi B+ (get the right form factor as the old RPi has to be “tilted” to fit in the case) and use the image as is. Good luck.