A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Greg Rudzinski
Date: 2018 Jul 25, 15:05 -0700
Here is a plan to get you out off your absurd predicament.
From your last fix plot a DR position for morning civil twilight. Assume the DR position is a known position. Precalculate the Hs for a selected body for the civil twilight time. Preset a hack watch to this time. Preset the sextant to Hs of the selected body. When the selected body is on the horizon at the sextant preset then start the hack watch. The hack watch can now be used to reset the chronometer. Longitude going forward will only be out by the error of the DR position (5 to 10 NM). I don't think a lunar at sea would do better.