There does not seem to be any hard or fast rules or case law on the situation you describe. You need to light a fire under the financial institutions, they have put you at risk. Go ahead with the re-contributions. Ask the institutions to void the subsequent Form 1099-Q, Payments From Qualified Education Programs. Remind them that they made the error that led to the issuance of this form.
However, be prepared for the result to be an early distribution. You will not be be charged taxes on the contributions returned to you, only on the increase and there will also be a 10% penalty on the early distribution, Again, only on the increase in value.
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