Hello
I think it is pretty certain that the different characteristics in the eagle design are all down to variations by the many manufacturers who produced these buttons over the years.
There are plenty of references on other sites to Admiralty Order No.2, dated June 1914, which stated that the badge of an eagle will be worn by members of the RNAS as the centre piece replacing the anchor on officers' caps. So clearly an eagle was the intended bird from the start. The idea of an albatross just seems to be a long-standing myth.
On a slightly different note, there was an article in Button Lines about the buttons of the Royal Canadian Mounted Police which illustrated the first 'buffalo' head pattern button used by the North West Mounted Police. Apparently when this design was introduced in 1880 the English makers had only a written description to go by and as many had probably never seen a buffalo before there are some very odd-looking creatures seen on these buttons.
Perhaps something similar happened with the eagle on the RNAS/RAF buttons! Maybe the engraver asked "What's an eagle?" and was just told "A big bird with a large beak"!
Roger