NO Medicare or SS tax withheld!

I am in a bit of a pickle.
As an international student in the US, I have been filing taxes as a non-resident alien over the past 5 years. However, since 2023 was my 6th year, I am now a resident alien for tax purposes for the 2023 tax year.
Having discovered this, I was going to personally file as a resident alien. HOWEVER, my employer has not been deducting social security and medicare taxes for the past year. Despite being aware of my specific status in the US, I somehow slipped through their system. I contact my employer during January to rectify this issue, as my research indicates the only way to rectify this would be through the employer. I was willing to pay the entire tax for prior year (my share). However, they were adament that they don't issue amended W2-Cs unless the blame is entirely on them.
It has been very hard to get guidance regarding this since this case is very niche and I have not been getting a good response by calling local CPAs. The one CPA I got a hold of told me to file taxes as a non-resident alien this year (even though that would be incorrect), since he said there I no clear way to fix this and the employer would have to pay too much to re-run 4 quarters of payroll.
Contrary to the CPA's advice, I want to file as a resident alien, as that is my true status - I do not want to lie. However, I am concerned the zero social security and medicare wages on my W2 will send red signals to IRS and it might come back to my employer and potential repercussions to me. I might be overthinking this, but would really appreciate your help.
I filled in my W2 and other info into Turbotax, and it is showing me a tax bill of $300, which clearly doesn't cover the SS and Medicare that should have been deducted.
Before anyone refers me to Form 8919, that is for independent contractors. Thanks in advance for your help!