Thanks, it looks cool!
I got a pair of OS transponders showing up in OpenStint with the firmware you provided. I initially flashed the hex I created but despite getting flashing light when powering it up, don't get any hits with the hackrf. I'll need to spend some time to figure out my mistake, but I have an idea.
It's a known phenomena. The transmission is timing-critical, and the firmware is using the SPI bus to do it. The next bit has to be available right when the transmit buffer goes empty. You have to compile with optimalization, otherwise the compiler keeps extra operations in the loop (to help debugging).