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Bill Ritchie raised an interesting question, at least from a theoretical point of view. Measuring the maximum altitude of a body and timing the moment of max, is it then possible to find latitude and longitude, even when the maximum altitude occurs slightly off the meridian? In most (all ?) practical cases it is not possible to time the maximum altitude with sufficient precision to get a reliable longitude. But in theory, yes it is possible.

You know the UT, thus you know GHA and declination. Also you know the altitude, and you know that it is at its maximum (or minimum, that should work as well). Thus the derivate of altitude with respect to time is zero and it is not that difficult to derive a formula giving local hour angle as a function of lattiude. As the LHA is a small quantity makes the formula quite simple. An approximate latitude is found by assuming that the body is on the meridian, and this latitude is used to find the LHA. As cos LHA varies very slowly for small angles, the found LHA will be quite correct. Using these data calculate the altitude and compare with the measured one. Adjust latitude until the altitudes match. Problem solved! You do not even need a spreadsheet or calculator. See attached file.
Lars