Hi Ben,
I want to make sure I'm understanding correctly what you are trying to achieve so please correct me if I'm wrong.
I have a couple additional questions concerning the I2C protocol. As a standard, each time a device receives a byte it responds with an ack/nack bit.

If I understood correctly, you want to send data from the radio to the LPC, correct? If this is the case each time you send a byte, the LPC will respond with an ack/nack bit. Does your radio have the ability to manage this acknowledgement bit? If not, it will affect the communication directly, since the LPC will be modifying the data line.
So keep in mind that if the above mentioned is your case. It will not be possible to follow through using I2C, in that case you would have to emulate the communication using GPIOs(although this might be more complicated and we dont have any examples of how this can be implemented).
I would suggest here to take a look at the MCUs that have the FlexIO. The FlexIO is a highly configurable module providing a wide range of functionality including: emulation of a variety of serial communication protocols. The Kinetis KL43 is a Cortex-M0+ (same as the LPC824) and does support FlexIO.
Best Regards,
Sabina