Adding to the mix is that this is an older pattern (very useful information, by the way!) and the different ways in which the term "4-ply" is used. In the UK, 4 ply is generally fingering yarn, which makes sense for such a fine gauge in this pattern. In the US, 4-ply is often associated with "worsted weight" (which is different from worsted in the spinning process, just to make it more complicated
) DK is a lighter worsted, and it would be very hard to get 7.5 to 9.5 sts per inch. If you have some DK and want to use it, you might try looking for a similar pattern with a gauge of about 5 sts per inch. You could use your original pattern, but you'd have to basically re-design the whole thing. If you do want to use the pattern, then try using sock yarn.