Past Pubs 590 and 590-A provide the contribution limit for each year, so contributions would not be more than the limit (unless excess contributions subject to penalty were made):
https://www.irs.gov/prior-year-forms-and-instructions
It's not really a solution, but waiting until age 59½ to take from your Roth IRAs any more than the contribution basis that you do know about, if any, would avoid the problem of needing to know the exact basis. The longer funds remain in the Roth IRA the more beneficial the Roth IRA is under the assumption that the Roth IRA will be invested in a way that produces gains.
Although your father might have retained the Forms 5498 on your behalf, they are part of your tax history, not his.
