You have an interesting little mystery here. I looked up Achsah Porter at family search labs and also Heritage questcensus. In 1844 Achsah Porter married William McKinstry in Athens County> I found her in the 1850 census with a Rebecca Porter living with her. Achsah was listed in her 60's so I'm going to go out on a limb and say this is probably the one you are researching. Later it seems she took back the Porter name as I found her living with Rebecca and Saml? Throckmorton in Athens county(1870 census). Now Jacob and Amanda Barnes Porter were probably related to Achsah as they had a daughter born in 1864 named Achsah Porter. If someway you could go through a backdoor to get your info--it might be the only way you will ever find ther names of her parents. I have tried cemetery records in the past and found they yielded very little info. My email now is firstname.lastname@example.org. I will sleuthe some for you!