Supposing that the residue responsible for the crucible adhesion to its support is indeed chiefly contributed by the said bismuth ferrite sample, and not by some other previous unnoticed contamination ― you may consider to attack that residue with either sodium tetraborate (Na2B4O7) or borax (Na2B4O7•10H2O) by ~745 ºC for some minutes; and after cooling, with conc. aq. HCl (room temperature). The crucible and its adherent support should be removed from the DSC equipment before the suggested flux attack.

You may want to check also: https://www.researchgate.net/post/How_to_clean_up_the_platinum_crucible_used_in_thermal_analysis

You could try putting liquid nitrogen in the pan and hope that the thermal contraction helps the pan pull away, or at least makes the adhesive material more brittle so you can force it out. Chances of success may be low, but it may be a good first attempt since it poses little risk to the instrument.