Try a borerus which is like an ad-hoc beis din.
A borerus should be cheaper, and most of the time much faster. Each side chooses a dayan (which, in a “treifa borerus”, can actively defends their side – or alternatively they both should be somewhat impartial) and these two dayonim each choose the third rav/dayan.
As someone above suggested, an even simpler solution is agreeing on a single rav/dayan (the now-classic “Let’s ask Rabbi Dayan” solution) and agree in advance in writing that you’ll both accept his psak. With this method, it’s often practical to put both sides positions in writing first and then have a 40 minute meeting with the rov where each side gets equal amount of time to speak and submit evidence. This ensures that it won;t drag on into multiple meetings or phone calls.