Huge Estate Tax Problem for 15 million dollar estate

For community guide lines we are louisiana residents.
My Siblings and I have been working on settling our father's estate. He passed away December 2017. To outline the major problem is that our father didn't file a 706 for our mother when she passed away in September of 2011. He simply just use the unlimited marital transfer to gain control of all the assets which was pretty common at the time for these types of estates. But this has left us very vulnerable to estate taxes. We are only able to claim the 5.49 million deduction that was allotted for individuals whom passed away in 2017. But the next year in January of 2018 the tax law to allow an individual to have tax shelter of 11.1 million and married couples could have up to 22.2 million in tax shelter for their heirs. We are considering using a alternative valuation date to be able to get secure the 11.1 million tax shelter, but are not sure if it is possible. We are also considering filing a private letter ruling to see if we could possibly claim at minimum the tax deduction that our father didn't claim for our mother which would be 5 million in addition to our fathers 5.49 million deduction would give us 10.49 million of shelter. Leaving us to only be taxed on 4.5 million or 4 million if we could secure the tax deduction for 2018 from my father. Currently from advice from our attorney's and cpa we either owe 8.1 million in estate taxes or about 4.6 million depending on how much penalties and interest the irs demands from the estate. We are at wits end trying to salvage as much of our parents estate as possible. My sister is in a very uncomfortable situation as executrix of the estate and doesn't want to be held liable for making critical mistakes as the situation she inherited was both good and bad also complex without the connection of other individuals who gone through a similar situation. We are a family of 3. Two brothers one sister, and both myself and older brother have children to support. My father had no debts owed. We don't mind paying taxes, but losing half estate in taxes on money that has already been taxed throughout my father lifetime seems absurd. Any help or guidance will be greatly appreciated.