Determining the appropriate bioconjugate
There are general guidelines for cross-linking protein-protein interactions, but specific parameters (i.e. cross-linker sub-types,  spacer length, linker concentration, reaction pH and temperature) are often determined experimentally. Common protein cross-linkers target reactive functional groups that are more likely found on the surface of the protein than in its "active site" or "interface" that is often buried.

Given your relatively hydrophobic, non-reactive binging motif (Tyr/Pro/Met), if you do not need a large amount of cross-linked protein sample, then you could label it with photoactivatable amino acid such as L-photo-Met. Since Met is not often found on the surface, internal cross-linking would stabilize your protein and its binding partner.

If you need a large amount of cross-linked protein (e.g. in mg) for further structural studies, labeling can be costly. You could possibly cross-link the protein (complex) crystal itself (since there were crystals as you mentioned), often just by glutaraldehyde. If the complex is there in the crystal, it would now be as solid as rock.