I recently went through a very similar deal. In my case, the owner of the tax sale certificate had recently obtained judgment against the deceased owner but was unaware their defendant was dead.
I contacted the attorney for the owners of the tax certificate and purchased their certificate and an assignment of the lawsuit they had going. Once the tax sale certificate was reissued in our name we became the unopened estate's largest creditor and for that reason we were able to open the estate. We had the prior judgment vacated, substituted ourselves as Plaintiff, I hired a separate lawyer to open the estate, be the PR, etc. We served the lawsuit to foreclose redemption on the estate and 10 short months later received the deed to the property.
The people you're trying to make a deal with won't be able to transfer the property if they don't open the estate. You should research the high bid premium to see what they're expecting to get from the tax sale process. Many large tax lien buyers are in it for the interest rate play, the last thing they want is to actually get a piece of real estate. They're not going to take a haircut for you, but you can get it very close to what they paid, their legal fees and all accrued interest.
The high bid premium is a circuit breaker to make sure the tax sale process rewards investors and penalized tax scofflaws, but stops short of the taxpayer being robbed of their property. If you look at the tax sale results you may have to find your winning bidder, their bidder code and then in the results its expressed as BidderCode and BidFactor. Multiply the bid factor by the assessed value in SDAT and that's the high bid premium. You pay that to the county after foreclosing the right of redemption and in your case it will get paid into the estate and distributed to its heirs.