I did a little nosing around, and find that your 'old family notes' have some factual problems.
1) There was a Capt. John Shether in the 2d CT Light Dragoons, but I can find no David Martin at all listed in CT rolls, or rolls for this Regiment.
2) No Capt. Asher F. (Fitz?) Randolph or Fitzrandolph is listed as a Captain in any NJ Continental Regiment. One Asher *T* (?) is listed as being with a NY Regiment, but I have not verified which one; it is a peculiar index listing not giving the right microfilm roll number. This person is not listed among the NY Continental Regiments ca. in published rosters.
3) A David Martin was in the 3rd NJ (Continental), as Pvt., Corporal, and finally Sgt. A young teenager would not have been given rank of Corporal or Sgt., and probably would have been drummer or musician.
4) The 8th CT (Continental) was not organized and working until April 1777, so was not involved in Defense of Boston (ended March 1776).
It is hard to understand how your source came up with most of the combinations of dates and names and regiments that you give.