Risks of burning melamine formaldehyde adhesives
I am by no means an expert in the pyrolysis of different woods by any means. But after spending some time reading through some papers for you, I found one which burns MDF in a slightly different burner to you (around 450-600C) and the ash produced contained formaldehyde at 1681 mg/kg.

doi:10.1016/j.enconman.2014.12.032 - incase you want a read yourself.

This document goes through different methods in producing biochars and says that providing the temperature of pyrolysis is above 500C, it shouldn't contain any PAH's or Dioxins within the biochar and if it does, it'll be several times lower than required clean up set by the Model Toxic Control Act.

Everything else I have read seems to not have specific analysis on what exactly is left within the biochar. There are plenty of organics released as gases during the process specifically above 500C which you could argue should no longer be in the biochar. Have a look around at papers, I know it's not a definitive answer but it might be a start for you.