Does anyone know how to replicate the "Open Sales Order" in the Reports section in a saved search? I'm trying the column "Amount unbilled" on a saved search but it's giving me different results.

Maybe try joining to the Billing Transaction node and summing that? Do you have Foreign Currency? I'm not all that familiar with Amount Unbilled, but I think unless an Amount field says otherwise, it's showing converted functional currency amounts.

I don't know of you can join the billing transaction in a salved search.

You definitely can. What is does though is force things to a line item level since the Invoicing transactions are linked at the line item level of SOs. So you'll likely have to do some grouping/summing.