This web page and comment by G&R Partners (a firm that provides payroll and benefits services to other companies, I'm not endorsing them, I found them in a web search) suggests that while an employer has no legal obligation to assist an employee after a benefits mistake, the IRS does allow some flexibility to correct mistakes:
Legally, employers are not required to do anything for employees who
have missed the open enrollment deadline. In fact, the terms of your
benefits plans may prohibit you from making exceptions for employees
who do not make benefits elections within a certain time period, such
as before the new plan year begins.
However, IRS officials have offered guidance that, where there is
clear and convincing evidence that an individual has made a mistake in
an election or that the employer has made an administrative mistake in
recording that election, the election can be undone, even
retroactively. These administrative errors include incorrect digits in
the Social Security numbers, or obvious typos. Theses administrative
errors allow an employer to change ONLY things that are directly
affected by the error.
So it seems that you have hope, but you need to convince the employer to go out of their way to assist you, which may be difficult to do since there's no legal obligation for them to do so, and they face some liability if they are not able to convince the IRS that this was a correction for an unintentional mistake.
I am certain that mistakes can be corrected after open enrollment because a data entry error by our benefits provider left me without dental insurance, I discovered it about a month after open enrollment ended, reported it to HR with a copy of my enrollment form showing that I selected the coverage, and they got it fixed with the benefits provider. But this one was easy to prove that it was a mistake since I had the form showing that I selected coverage.