Can I enter/link multiple 1098s for a single property (different banks) refinanced in 2020 and retain original origination date (2016) to preserve interest deductibility?

Yes, you can enter multiple 1098s from different banks for a single property.  Enter them one at a time. After going through the interview steps with the first lender, you can add the second one when you get to the Mortgage deduction summary screen.  In the case of a refinance, it's best to enter the 1098 from your original loan before the 1098 from your refinance.  This will help the software to recognize that the origination date of the loan is pre-2020.

That's important because as you mentioned, [only] the acquisition debt remains deductible.  The loan origination date section should present itself correctly when the software recognizes that you've entered two 1098 forms.  

Here's how to enter your mortgage interest statement in TurboTax:

1. With your return open, search for 1098 and select the Jump to link in the search results.
2. Follow the instructions to enter your 1098 info.