Those sure are fascinating letters Johnston left us.
I would submit that any interpretation on this recon probably needs to start with what Lee meant by "there".
You also should take a closer look at this whole sunrise issue, and what time sunrise was. As noted by two earlier posts, there was no daylight savings back then.
As for the GB Mag 61 article mentioned above, I highly recommend it. The author stuck to interpreting primary sources, just like you're trying to do here - and more to the point, proposed the same route that you are suggesting Johnston took in your post above.