HSA and Medicare

Greatly appreciate some advice:  I delayed Medicare enrollment so  I could keep contributing to  my HSA.  I enrolled in Social Security and Medicare effective January 2021 -- the month I turned 66.  I knew about the 6 month retroactive period for Medicare A, so I thought I could  contribute to my HSA through June 2020.  However, I started my application process in September, and found that because of this, my Medicare A was retroactive to March 2020.  So, definitely any contribution from March to June is now ineligible.  Then, to make it worse, I discovered the pro-rated allowed contributions based on months of eligibility.  So, my question:  if I understand the IRS correctly, I would only be allowed two months of eligibility so my limit for 2020 would be 2/12 of ($3550+$100) = $758?

Bonus question:  if my 2020 contributions were from me and from my employer, do I need to submit two requests for adjustment -- me directly to the fund and me to my employer?