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With the bar point made (as in Timothy's position) it's a completely different situation: if we hit (13/4*) our opponent can play his entering sixes safely (13/7) because he has his bar pt closed.(He shows diagram of Tim's 61P-61P-63Z-54.)
The 6 factor you addressed is sometimes valid, but I don't think it means much when applied to these positions.
Firstly, in the two above diagrammed positions, if Black hits (13/4*), White will play 63 and higher 6s the same way (running the lead back checker or fanning) whether Blue's bar point has been made (i.e., with 61P) or not. It would be better to strike those rolls from your comment.
That leaves the variations where Blue hits and White rolls a 61 or 62. Believe it or not, whether Blue has made his bar point hardly makes any difference:
According to Snowie evals, on the left, after Blue hits 13/4*, White's play of bar/24 13/7 is only .016 worse than bar/18, and bar/23 13/7 is only .025 worse than bar/18. These rolls occur 1/18 of the time, so that effect is .041/18, which is just over .002.
Not only that, but on the right, if Blue's bar point is made (with 61P), it actually costs White more than on the left! Having to strip the midpoint and stack a fourth checker on the 7pt is on average more unbearable than slotting the 7pt; bar/24 13/7 is .037 worse than bar/18, and bar/23 13/7 is .015 worse than bar/18. The effect is .052/18, which is just under .003.
It's tiny in any case (and the evals may be sloppy), but the effect of 61 and 62 suggests that Blue actually has slightly more incentive to play 13/4* in Tim's position (the above right diagram but with Blue 61P added) than in 61P-43Z-54 (the above left diagram but with Blue 61P added), a contraindicative factor as H is actually worse. And the other 6s are basically irrelevant. Sorry!
Nack