Given a handheld GPS with an accuracy of roughly 2 meters (verified through field tests) and an observation with an HDOP of 1.2, the accuracy of that one observation should be within 2 meters X 1.2 of actual horizontal position, correct? Where can I find documentation of how this works? That is documentation that shows reported device accuracy multiplied by the HDOP yields horizontal accuracy.
DOP relates the User Ranging Error (URE) to position coordinates error (PCE):
PCE = URE * DOP
It seems you already determined both PCE (2 m) and HDOP (1.2). The only unknown left is URE, which is this case equals URE = HPCE / HDOP = 1.67 m.
Now with that information at hand, you can assume the URE will not change, then predict the PCE of interest given DOP predictions, as given in GPS survey planning software.