If I have non-covered capital gains. and do not have a record of investment cost, how can I arrive at a cost for tax?
You need to enter a reasonable and good-faith estimate of cost basis. The IRS is receiving the 1099-B information from the broker, but is relying on you to report the correct category and/or cost basis. Otherwise the entire proceeds will be considered gain.
(It would be unreasonable for the IRS to claim you did not pay anything for the investment (Cost basis = "0", total proceeds taxable). It would be unreasonable for you to claim the total proceeds as the cost basis (no taxable income).