Hi @chooks,
Are the original wiring instructions correct (Vcc->ground, GND->3.3V)
the original wiring instructions are definitely wrong. In digital electronics, the ground and Vcc are never swapped. It seems to be a copy/paste accident in that final wiring instruction (ping @Lazar-Demin, I guess that's a typo worth correcting quickly). Everything else above looks correct.
The photo also seems to be correct, hard to really definitely tell but it seems I see the black GND wire go to the blue rail and the red one to the red rail on the breadboard.
Since I powered it in both directions (one of which being wrong by definition) what is the best way to tell if I fried the chip?
Probably the chip is fried (otherwise the setup should work).
Does the Omega start when the breadboard is connected the correct way (Vcc->Vcc, GND->GND)? Only the LEDs not working?
If not, then the chip is definitely fried (draws too much power and probably gets hot)
If Omega does startup, it's hard to tell because there are all sorts of semi-fried states the chip can have now - but most likely not working 100% ok any more.
If you have an easy means to get a replacement (~$1), I would continue with a known-good new chip to see if it works then.
PS: if you eye some home automation eventually, you might want to look at this