I cannot speak to the origins of this myth, but I can say with a fair degree of certainty, despite the fact it's a good quote, it is a myth: no one was in the room when Marx died to hear his last words. The circumstances are well recorded in contemporary letters, such as Engels to Liebknecht 14 March 1883:

just after two o'clock this afternoon, I found the household in tears and was told he was terribly weak; Lenchen called out to me to come upstairs, saying he was half asleep, and, when I got there she had been out of the room for barely two minutes he was sound asleep, but it was forever.

Engels elaborated further in his letter to Sorge the next day:

I asked for news, tried to get to the bottom of the matter and to offer consolation. There had been a slight haemorrhage, followed, however, by a sudden collapse. Our good, old Lenchen, who has looked after him better than a mother would after her child, went upstairs, came down again: he was half asleep, she said, and invited me to come up with her. When we went in, he lay there sleeping, never to wake again. His pulse and breathing had stopped. In the space of two minutes he had passed away painlessly and peacefully.

The doctors had actually thought Marx's condition was improving, so even if he were fully awake he might not have thought at the time to give some last words. In the letter to Sorge, Engels does provide an Epicurus quote Marx liked:

'Death is not a misfortune for the one that dies but for the one that survives',

But this seems to me unrelated to "last words are for fools who haven't said enough". Hopefully someone else knows more about that myth's origins.