My question to you is, "will you be under another HDHP policy at some point in 2021?"
If the answer is No or Probably Not, then there is nothing you can do except withdraw as much of the excess as you can (the $40), and carry over the remaining $376 to 2021. Yes, this will be dinged 6%.
This amount will carry over year after year until you can qualify to make HDHP contributions again. At that point, you will reduce your HSA contributions so that the $376 can be "charged off" against that year's annual HSA contribution limit.
What happens if you never get another HDHP plan? When the amount in your HSA drops to zero, the 6% penalty drops to zero.
If the answer is Yes, then you can contribute $376 to your HSA under the 2021 limit, yet ask that it be withdrawn as the 2020 excess.
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