Knowing people who were his students, and having met Jan Karski myself several times, I can assure you that for the longest time, until Lanzman dragged him out of his "cave," Jan Karski was a very tormented man who preferred to forget what he saw, did, experiences, and the frustrations and helplessness of the failure of his mission.
In what way did Karski's mission fail? In 1942, his mission was to bring back messages from the Polish Underground, uncluding two Jewish leaders, a Bundist and a Zionist as I recall, to the Polish Government-in-Exile in London. He succeeded in that mission; he brought the messages back, and reported to his superiors.
In 1944, he had the mission of preparing propaganda to support the position of the Polish Government-in-Exile, which was under threat from the Soviet Union and the rival Communist Government sponsored by it. In that he was also successful; he produced the book "Secret State", which became a best-seller.
In the 1990s, the idea was propagated that he had a mission of trying to save the Jews of Poland, that he failed in that mission, and was devastated as a result. But he had no such mission! There is no evidence from the reports he made back to the Polish Government-in-Exile that he had any such mission.
The sole Jewish element in his mission was to carry the message from the two Jewish leaders in Warsaw. That message was that the Jews of Warsaw were being deported, and that the Polish Government-in-Exile should publicise it. But it was not a message from Karski; he was merely the messenger boy. And the publicising of the message was carried out by Szwarcbart and Zygielbojm (including material from other sources), not by Karski; their report was published in the 1943 book "The Black Book of Polish Jewry".
It was not until 1944 that Karski incorporated the Szwarcbart-Zygielbojm report into his book "Story of a Secret State", and falsely claimed that it was based on his owm personal expereince, ie that he had been into the Warsaw Ghetto and into Belzec, and witnessed what was going on there.
When I say "falsely", I do not mean that he was telling a deliberate lie. It may well be that the Polish Government-in-Exile, for whom he was writing the book, had ordered him to present the Szwarcbart-Zygielbojm material as if it were something he had witnessed himself, in order to give it more "shock value" to the readers.
I agree that Karski did not immediately begin to promote himself as someone who had "tried to stop the Holocaust". In the 1950s his main role seems to have been as a propagandist against Communism for the United States Government.
However, at some point, apparently in the 1980s, he began to revive the account of his activities given in "Secret State", and to claim that he had had a mission to rescue Jews. It may be his involvement with Lanzmann, who must have been made aware of Karski through "Secret State", that motivated him to do so. Whatever the case was, it was from that point on that he began increasingly to promote himself as a rescuer of Jews.
By the way, I do not buy the explanation in the Woods/Jankowski book, that Karski's description of his penetration of an extermination camp is true, but that it was Izbica Lubelska, not Belzec.
The camp at Izbica Lubelska was a transit camp for Jews deported from Slovakia. However, Karski claims that the camp which he claims to have visited in disguise, and which he identifies as Belzec, was one to which Jews from warsaw were sent. That description is clearly based on the Szwarcbart-Zygielbojm report, which describes the deportation of Jews from Warsaw; it states that they were sent to a "sorting camp" (oboz rozdzielczy), and after a short stay there, onward to an extermination camp which Szwarcbart and Zygiebojm called Belzec. They got the process right, but the name wrong; it was actually treblinka to whoch the Warsaw Jews were sent from the "oboz rozdzielczy".
Karski simply repeats the misidentification, except that he gives the name "Belzec" to the "oboz rozdzielczy" itself. Since the sorting camp was on the way from Warsaw to treblinka, it cannot have been Izbica Lubelska.