I look forward to seeing the docs you are sending. I dug in my files and found a few things that may help clarify things.
The Pension Act of 1832 (4 Statute 529) stipulated that an applicant had to prove two full years of service to qualify for a complete pension (i.e., full pay). Service more than 2 years made no difference with regard to the pension award.
It appears that his initial application dated Sep 1832 was rejected for some reason(deemed invalid). In Jun 1833 William provided an amendment, and his application was subsequently approved and issued in July 1833 at Wythe Court House. I assume $80 per annum was full pay, and they also paid two years in arrears plus an additional prorated sum ($160 + $40).I would think $200 was a tidy sum in 1833. Under the 6th April 1836 act (the "Lost" Pension Act), the balance of his annual payment was made into his estate up to March 1837 when he died.
From reading both applications it is still not clear to me why the initial one was rejected, but I have read that there were many applications routinely rejected for claiming spy service because it was difficult to prove and prone to fraudulent claims. Maybe you can see what it was that kicked William's back?