In my opinion it's quite clear that Hartmanns claims are several times too high.
Following indices (not prooves) speaks for this.
1.) From July 1943 up to the end of war, there were no longer eyewitnesses needed to confirm a kill. Instead of, the kills should be checked "after the war". But this is the time made most of his kills.
2.) Already in 1942 german Pilots like Graf and Dickfeld overclaimed several times.
some examples:
13.5.1942 Luftwaffe claimed 65 kills, of these 42 belonged to JG-52; but VVS lost in reality only 20 planes.
14.5.1942 claimes by III/JG-52 47 kills,
out of these were: Graf 6 kills; Grislawski 2 MiG-3; Dickfeld 9 kills.
Indeed VVS lost 14 planes; 5 Yak-1, 2 Il2-2; 4 LaGG-3 and some biplanes.
4.) Günther Rall fights at least one of Hartmanns claims, described in Tolliver/Constable.
5.) Hartmanns was highly interested to become a hero (not such a untypical behaviour for fighterpilots), which gave him also not a well reputation by his comrads.
6.) In accordance to 5.) Hartmann everytime has his best days, when he was "close" to the 200 or 300 kill border
.
7.) In accordance to 6.), when Hartmann reached the 300th kill, he was awarded with the diamonds next day. No "long and strict confirmation procedure" was suddenly needed.