The lattice mismatch of thin films doesn't cause pressure though. The mismatch causes biaxial stresses and the out-of-plane stress is zero. On top of that typical thin films fracture or delaminate at 100 MPa to 10 GPa stresses, not nearly close enough for 2.8 million atmospheres of pressure (284 GPa). Formation of misfit dislocations between the different crystals would prevent such stresses as well.

Doping or alloying with impurity atoms, on the other hand, can cause pressure or hydrostatic stresses, when a film is clamped to a substrate. 284 GPa would be very high but maybe not impossible. Though introducing impurity atoms would likely ruin the superconductivity.