Unable to determine cost basis

Not an expert but if I had this issue and I would attempt to figure out which year (or maybe month and year) I acquired them and then either take the average price and use that, or I would pick the lowest price and use that. I would document how I arrived at the number. I also would retain the emails or mailings that show that the financial institutions had no history. Picking the average price or lower would probably show that you did your best to calculate the price without trying to cheat.