I would just like to make a couple of points on the use of Omega functions
First if you plot them as Log (Omega) they are much easier to read - superior portfolios can usually be identified visually.
Second optimisation around a single threshold may be done, (and you have illustrated this) but if you want to compare to Markowitz-type techniques, then you meed to consider the global position and that involves optimising the whole function.
Bill and Ana published a number of short pieces on how that might be done using metrics of the function.

Con Keating