Hi Martijn,
Not sure about the exact situation you are facing, listed below please find some of the suggestions I can think of:
1. There are soft uart implementations on github, which you might be able to port to zephyr;
2. If you got SPI interface on your module, there are bridge modules available to convert i2c/spi to uart; // sc16is740 etc
3. If you only care about the application level log, probably you can use bluetooth to build a virtual serial port for logging purpose;
Best Regards,
Jian