Without due process of law can be interpreted in several ways. Trial by jury or judge or act of legislature, as in 10th Amendment and enumeration of those rights not specifically listed granted to the states, but that wouldn't have bolstered your case.
Fifth Amendment, reasonable argument. 14th Amendment, post-Civil War apologetic, PC-mumbo-jumbo.
Posterity is can be parsed in several ways. These were learned men who were well away of the impact of history. Posterity could simply mean the light in which this great nation would be viewed 2000 years hence. it could also refer to the offspring or those who would be citizens at a later time.
I did take the time to look at each of the seven definitions listed at Webster's (I believe) On-Line and in the context of "blessings of liberty for our posterity", yours was the proper context.
Sweet. Now if we could just get some politicians and judges who didn't have that part excised out of their copies.