Concerning the asymmetrical distribution of the southern “icy” craters which you note, compare that with the distribution map of _northern_ craters bearing ice mounds — on p. 4 (p. 177) of the foregoing Icarus paper. Looking at that, I’d say their distribution is not particular symmetrical either — particularly when examined closely.

Notice crater Korolov, for instance, choked with ice despite its low 70’s latitude — then there’s crater Louth, actually at 70 degrees latitude. Also, FYI, here’s a great shot (taken by Mars Express) of crater Korolov’s 3,848 cubic kilometers (according to the Icarus paper’s Table 1) of ice!

One might additionally peruse the explanation(s) proffered for the existence of the sizable ice mounds placed within certain high-latitude northern-hemisphere craters, as laid out in section 4 — beginning on p. 10 (p. 183) of the Icarus paper. From the text, it appears that the only viable theory explaining the (northern martian crater) ice-mound phenomenon is (as described in section 4.5) martian “craters as cold traps.”

See in particular the paper’s explanatory Fig. 15 — appearing on p. 17 (190).