NavList:

I had one more crack at this. Rather than try the double altitude calculation again I used the mid point between NY and Hamilton (36N 71W) as an AP then plotted all three sights. This gave an intercept off the scale so I recast it with an AP of 35N 71W which gave a nice cocked hat (too good to be true) at about 34d55N 71d28N. As there's only a 45d spread of Azimuth centred on East this is not good for Latitude IMHO. Obviously Longitude is suspect as we don't know the time reliably. I can't face the double altitude problem right now but feel that would give a more reliable estimate for Latitude. The intercept is well N of Bermuda and S of NY so let's use that and think about Longitude.

An AP near to the intercept at 35N 71d30W was used as a start point then Hc/Z calculated for an AP =30' more East at 71W and 2 mins earlier, stars stayed the same as expected but the Moon got higher. Repeated with 30' more West at 72W and 2 minutes later. This was closer and and moving to 72d15W at 225500UT was better. At this point it seemed near enough to know where I was within about 20 miles which is adequate for finding Bermuda. I'm somewhere near 34d55N 72d W at about 225500 UT on the 30th. 

Moving East by 30 arcmins and 2 minutes earlier makes about a 1 arcminute altitude difference to the moon, the reverse if West and later. If I'm confident in measuring the altitude to within an arcminute then I know Longitude to about half a degree but let's say a degree to be safe. This only works if the Moon is visible and rising rapidly. I feel like I've gone wrong somewhere as this partly solves the Longitude problem. Whilst the Moon helps with Longitude there won't be any evening sights of it after the 30th, too low for reliability (I think) on 31st and none on Feb1/2. Might get some morning sights but who knows. This didn't seem too many iterations, there might be a way of doing a reverse look up in the air tables.

Regarding the Full Moon then there is clearly a relationship between Sunset and Moonrise. If the Sun has set and the Moon hasn't risen then it's past full, if the Moon is just risen before Sunset it's Full. This might not apply in the tropics or polar regions - don't know.

I'm nearly back in NY now, hopefully it's warmed up. Good problem Frank, I think I learned a lot if I got it right, now need to find a sensible way of solving the Double Altitude problem, it's hard work.

BobC