I have a carry handle that measures 0.793" thick on the rear of the sight, and has a "BK" forge mark.  I need to know if this the correct carry handle for an "F" marked front sight on a CAR/M4 upper.

No one knows this?

Man, this whole F marked thing has gotten carried way beyond the realm of sanity in recent times.  If your top assy is in spec, the F marked base will work fine, and IT DOESN"T MATTER WHOSE "SPEC" IT IS,

Now I don't have an F type base, but my Rock Rivered flat top, with a  Bushie Sight assy, needs the higher sight point; so I use the Bushie .04 higher post which gives me a sight point exactly the same as your F base w/a standard post. If you have an F base, use a standard sight post and for pity sake, don't worry about the height of the rear base.

My Colt SP1 carbine  came with a .04 inch higher post in 1978.  All carbine and SMG types have always needed a higher front sight point-----and the Johnny come lately "experts" on this site who spread the BS that only flat tops need them simply don't know anything about AR15/M16 short barrel sight history.

As far as I (and some others on this site) can tell, the F type front sight base came into existance only because the military wanted to only have to deal with one front sight post height for the M16s and M4s. Until the adoption of the M4, short barrelled pieces were only used by special units, and armorers in those units didn't have an issue with two different height fronts. When the M4 came along as standard for the Army, with the Marines keeping the M16A2 and most reserve units still having the rifles, it was just easier to go to the higher base to keep one post height.

To repeat myself, just go ahead and use a standard rifle sight post on your M4gery if you have an F base on the barrel.  If it shoots a little low w/the sight unit you have just crank the blade down a few clicks.  That's what that spring and plunger are there for