I happen to have a decent number of LPC11u35 parts on hand. The IBDAP firmware turns the LPC into an OpenOCD-compatible CMSIS-DAP debug device capable of programming other things over software SWD.
So, flash my fork of the IBDAP firmware to the LPC using the USB drag and drop bootloader, and you can then debug the nRF chip.
nRF chip listens on UART for keydata and simply transmits it when received, so you shouldn't need to debug it very much, and you can use the 10-pin header to enable debugging the LPC chip which is doing the heavy lifting.
I may set things up so a specific key sequence will make the IBDAP application run, and include it into the binary of the actual KB firmware, but it will come down to flash size.