What happens if I can't fully determine the basis of a Coverdell ESA distribution?

In 2017, I received a distribution for my daughter's Coverdell ESA.

The distribution was used entirely to pay for eligible college expenses (which I can prove), so that's not a problem.

The problem is that I can't fully recreate the basis of the distribution.

I have custodian/brokerage (etc.) records going back 20 years, but I still have a couple of gaps in between where I don't have any records. I have Form 5498 from various custodians, so that helps. Some of these custodians are no longer in business.

Can I just use the Form 5498s that I do have and report that as the basis? Since I used the entire distribution to pay for eligible college expenses, I shouldn't be taxed on the distribution regardless of the true basis. Or what do I do?

Thank you.