I’ve never seen an agreement that specifies a specific Beis Din, but I guess it can exist. But that doesn’t neccesarily mean there is something underhanded going on. It may just mean that they don’t want a run around to decide on a Beis din.
I have seen a number of agreements that specify specific arbitration groups. I’ve seen these in contracts that had no Jewish parties. Do you assert the same allegations in such cases or do you limit it to botei din?