Four of those straight flushes in your calculations are royals. Would that make a difference?
I am now trying to determine where the wiki page's second number comes from: 332,220,508,619 to 1. It states the number is for when both hands occur in the same deal. However, I think it was shown conclusively above that the actual number is much smaller than this. So then, where does this 332,220,508,619 number come from?
One guess is that it is the probability of getting a full house with the pair only contained in the straight flush. Using the numbers from above, this can be calculated as:
(40/2,598,960)*(480/1,533,939) * 2 = 1 in ~103,818,909
This is a bigger number but still far off from 332,220,508,619.
So now try and get an upper bound on the total number of all possible hands. I think this can be estimated simply as:
(1/2,598,960)*(1/1,533,939) = 1 in 3,986,646,103,440
Well, this now is a larger number than the the wiki number but only 13 times or so. Something tells me that as rare as the situation is it is not so rare as to be only 1/13 times smaller than all possible hands.
So now I think the referenced source in the wiki article is suspect.