NavList:

Well, this is where camera view collides with single point perspective with the Moon at almost infinity.  Father Ted could have described it perfectly. https://www.bing.com/videos/riverview/relatedvideo?q=Father+Ted+big+cow+small+cow&mid=9AA71EF98F6C552C3B499AA71EF98F6C552C3B49&churl=&FORM=VIRE

First impressions: 
1.  It’s within one day of the full Moon.
2.  Full Moon in November 2007 occurred at 14:30UT on 24Nov2007, with the Moon positioned 357,545 kilometres (222,169 miles) from Earth. This full moon was also classified as a Supermoon, meaning it occurred near the Moon's closest approach to Earth (perigee), making it appear about 7.53% larger than its average apparent size. Traditionally, this full moon is known as the Beaver Moon, a name used by North American Native populations to mark the time for setting beaver traps before winter.*
3.  24^th Nov 2007 was a Saturday.  The military prefer not to fly at the weekend, so we might be talking about Friday 23^rd Nov 2007.
4.  The brightest side of the Moon appears to be on the right.  This suggests waxing and agrees the Friday 23rd possibility.
5.  The shadow of the engines against the Bear’s fuselage means the Sun is almost horizontal with the aircraft.  Therefore, allowing for dip and refraction, the sun’s altitude will be very low, perhaps as low as 0° suggesting it’s just after sunrise or just before sunset.  The military love early starts emanating from ‘standing to’ in ‘days of yore’, so we’re probably looking at just after sunrise on Friday 23^rd with a possibility of just after sunrise on 24^th.
6.  The fighter is a F22A Raptor with the base/unit letters of AK on the LH vertical stabiliser indicating the 3^rd Fighter Wing of the 11^th Air Force normally based at Elmendorf AFB, Alaska.
7.  The Bear wouldn’t wish to stray too close to US territory, so from the Atlas, let’s pick an assumed position of 60N 170W. 
8.  Also from the Atlas, The International Date Line gets a bit bent between the US and Russia in the area in question, so that might affect the date finally chosen. 
9.  ‘Stellarium’ would be best to view this situation, but I can never get the correct lat & long in.  Therefore I’m stuck with ‘Navigator’.
10.  23^rd Nov doesn’t work between 19.30UT and 20.00UT.  The Moon Sets just before the Sun rises.
11.  24^th Nov would work around with the Sun at 0d 55’ and the Moon at 5° 5’ at 20.00UT, but the Moon could do with being a bit higher.  Taking an assumed position of 60N 179W would push the Moon a bit higher, but that doesn’t tie in with the information accidentally revealed on the Wikipedia F22 page which states that the aircraft were close to Nunivak Is (166W).  Let’s try 25^th.
12.  25^th Nov looks better with the Sun at 0d 40’ and Moon at 12d 38’ at 20.00UT, but that hits the waxing theory on the head, because the Moon would be waning.
13.  Unfortunately, I can’t show the Sun when it’s below the Hc=0· in ‘Navigator’, but taking time as 19.45UT would push the Moon up to 6°19’ on 24^th

Conclusion on time:  I’ll go for 19.45UT on Saturday 24^th November 2007, I.E. just after sunrise
That’s all for the moment.  I’ll go for the ‘big cow, small cow’ thing next time.  DaveP 

*the skylive.com