The son in the article, nine months into the process of clearing his parents' house, estimated he is one-third done. That's a lot of mental and physical work he inherited, or alternatively signed up for.
I cannot believe it is necessary to be so persnickety about it that it causes you stress and bitterness. Give your siblings a day to grab anything they want, then rent a dumpster and a wheelbarrow and go to town. Throw away everything you can force yourself to, one room a day. Dad's dead, he won't care. If it takes nine months, you're doing it wrong.
You can just use a service to take care of the estate, you are not obliged to do that at all.
That's assuming they've got money to pay for it after funeral expenses, et al.
They've had this house for 9 months. They're paying money to keep it, whether it's rent, mortgage or property taxes.