A 24 or 27mm in a typical 8" F/6 dob will yield merely 50x and 44x respectively. Not adequate magnification for M13 and for globulars in general, all you are going to see is a fuzz ball, and that's not what observing globulars is about. This is like getting a 4mm eyepiece to view the Pleiades. You'll be missing the true beauty of the object. These focal lengths are best left for larger open clusters, nebulae and sweeping the Milky Way.
Globulars are meant to be split open, which means magnification. An eyepiece of 7-9mm would be an ideal choice in an 8" F/6 dob. Get in close enough to actually resolve M13, but still frame it nicely. Lots of options out there... Delite, Delos, Nagler, Morpheus, ES and the list goes on.