Wow! Have just caught up with this string. Good to see so much interest in frigatebird id!
I have no doubt that this is a first stage [=juvenile] Lesser Frigatebird, as originally identifed by Geoff and concluded by Tung.
The diagnostic feature is the white axillary spurs leading forward from the front edge of the more or less triangular white underparts. In Christmas Island the spurs would be set further back and the white patch would be more diamond or oval-shaped. In addition the bill is not long enough for a Christmas but just right for Lesser. With the extra pics showing it scrapping with the Black Kite, it can also be seen to be not that much bigger and certainly not as large as a Christmas or Great would be in direct comparison. Lastly, the alar bar [the pale area across the upperwing coverts] is not particular conspicuous or well marked. That is just right for Lesser whereas Christmas would be much paler and more extensive.
Mike Chalmers