Education

To avoid the penalty tax, I believe the distribution must match the expenses (or exceptions to excise tax) of the coordinating year OR THE PREVIOUS YEAR if the distribution is made within the first six months of the following year. 

Therefor I believe you could make a distribution before June 1 2022,  to cover expenses for 2021 and 2022 and not pay the penalty on that distribution. 

The beneficiary could continue to take distributions until age 30 in which case the distributions would be taxed at her tax rate. 

The account could also be rolled over to a family member. 

However, if the transfer as been made, those options are no longer available. 

ADDITIONALLY you do need to have the basis and earnings reported separately so the tax is only based on the earnings portion. I  think the transfer to a brokerage account is considered a distribution, not a roll-over. 

According to the IRS:

"The excise tax doesn't apply if excess contributions made during 2021 (and any earnings on them) are distributed before the first day of the sixth month of the
following tax year (June 1, 2022, for a calendar year taxpayer).
However, you must include the distributed earnings in gross income for the year in which the excess contribution was made.

According to the IRS:

"Generally, distributions are tax free if they aren't more
than the beneficiary's adjusted qualified education expenses for the year. Don't report tax-free distributions (including qualifying rollovers) on your tax return."

"Adjusted qualified education expenses (AQEE). To
determine if total distributions for the year are more than
the amount of qualified education expenses, reduce total
qualified education expenses by any tax-free educational
assistance. Tax-free educational assistance includes:
• The tax-free part of scholarships and fellowship grants
(see Tax-Free Scholarships and Fellowship Grants in
chapter 1);
• Veterans' educational assistance (see Veterans' Benefits in chapter 1);
• The tax-free part of Pell grants (see Pell Grants and
Other Title IV Need-Based Education Grants in chapter 1);
• Employer-provided educational assistance (see chapter 10); and
• Any other nontaxable (tax-free) payments (other than
gifts or inheritances) received as educational assistance.
The amount you get by subtracting tax-free educational
assistance from your total qualified education expenses is
your adjusted qualified education expenses (AQEE). "

"Members of the beneficiary's family. For these purposes, the beneficiary's family includes the beneficiary's
spouse and the following other relatives of the beneficiary.
1. Son, daughter, stepchild, foster child, adopted child,
or a descendant of any of them.
2. Brother, sister, stepbrother, or stepsister.
3. Father or mother or ancestor of either.
4. Stepfather or stepmother.
5. Son or daughter of a brother or sister.
6. Brother or sister of father or mother.
7. Son-in-law, daughter-in-law, father-in-law,
mother-in-law, brother-in-law, or sister-in-law.
8. The spouse of any individual listed above.
9. First cousin."

Pub 970