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I was amazed that I was able to get my engine to run for well over
two hours. Has anyone else out there been able to do the same? Part
of the trick (I think) was to use a small mouthed insulated container
for the hot water.

Here is a video of my engine running for two hours twelve minutes
(time lapse at 1 second intervals). *WARNING* this file is 17 Meg.
http://www.stirlingengine.com/users/Gri ... inutes.avi

Obviously it is necessary to minimize heat loss from the "coffee cup" if a longer run is desired. A quart or larger thermos bottle with a mouth surrounded with a doughnut shaped piece of foam insulation to minimize heat loss from bottom plate of displacer chamber should give a run of longer time. A greater challenge would be to obtain a longer run with a standardized cup and quantity of hot fluid and it's temperature. This might involve some 'tweaking' of various parameters in the engine itself.
s/Stan