Indeed, it is possible to achieve performance which improves significantly on the column comparisons. We can find the location of all positive minimum values returned by a subscript reduction operator. So, we can use

/** location of row min GT 0 **/
t0 = time();
ndx = loc(x[ ,>< ] >0);
tloc2 = time() - t0;

For matrices of the various dimensions suggested, the method which I suggest is three to four times faster than the column comparisons process (with time specified by tloc).