Let me be sure: did your husband have the HSA in early 2020? And now in 2021, he has another HSA?
So he has not closed out his old HSA, right? Then he can contribute as part of his 2021 annual contribution the $376 to his OLD HSA, then immediately turn around and withdraw the rest of the excess amount before May 17th, so there will be no 6% penalty at all.
Note that since he has two HSAs, there is only one limit for the two of them - that is, you can't contribute $3,550 to one HSA and another $3,550 to another HSA, because you have in essence a single "virtual HSA".
This means that the $376 contribution will count against your 2021 limit, so be sure not to overcontribute for 2021.
Yes, you can try to carryover the excess amount and use it up in 2021, but that won't avoid the 6% penalty.
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