Chris is right, for vertical stacking you have to change the source order. That won't hurt your layout, because omega still floats to the right.
Also, "@include span-columns(12 omega, 12);" is a messy way to do things. Block elements span the full width by default, but this floats them, and sets the width explicitly, which is just bloating the code.
Best option is mobile-first - you won't need any code for the mobile layout.
If you still want to do desktop-first, all you really want to do is remove the previous layout:
@include at-breakpoint($tablet) {
#left, #right {
@include reset-columns;