I was rereading the information you have in your query. First I have, in all of my endevors to research Azariah Grant b 1748/49 at the latest, found nothing to tie him to Azariah Grant b 1722, I do have a strong suspicion he is the father. If he is it would more likely be by his first wife Eunice.

Azariah Grant b abt 1748/49 d 20 Feb 1819 is the father of Azariah Grant b 1782 who m Phoebe Vose.

Azariah Grant b abt 1748/49 d 20 Feb 1819 is buried in Dewey/Wright Cemetery, near Berlin, Washington, VT, USA. Tombstone record says he was 71 years of age. Even if he had just had a birthday and taking into consideration double dating, it would at most make him b in 1749.

Tombstone records can be wrong and Azariah and Abigail did have an unnamed child early in their marriage. That calls for some consideration. Unnamed usually but not always says died at birth or very soon after. hmmm!

Your Azariah Grant 1750-1822 I have not found any record of his birth or death.

Anyway good luck. Al