Are there any mature circuit board technologies that could withstand 300 °C?
Just so nobody is left wondering about the answer in the future thanks to suggestions in the comments section I have found that ceramic PCB technology exceeds my requirements.

Anyone interested in the topic should take a look at the paper
 Developing 300°C Ceramic Circuit Boards, Randy A. Normann, Perma Works LLC, 2015, which gives a report on the development of a circuit designed and built to monitor geothermal wells while being immersed in temperatures exceeding 300 °C and tested up to 550° C without failure (my application only requires a single surface to be in contact with the heat which seams trivial now in comparison).