Please be aware, what works on one vehicle will not necessarily work on another. Falkens being one in particular, there are members here that have them on other cars, and then fitted them to the omega with very different results. On the omega straight line stability is the handling key.
Falkens are exceptionally quiet though, but on this car that's where the good news ends.
But for the op. I would concentrate your efforts on worn chassis components and set up. Then worry about tyres tbh. Reason being if there is a fault on the car, the tyres will soon degrade to the same level and your back to square one, no matter what's fitted.
Sorry but i have to dissagree with your comments about falken tyres as i have used them on a few vehicles and know of alot of others using them on a wide range of vehicles and not one has had any problems with them, infact all feedbacks been very positive, most people overlook falkens/toyo's etc as they are alot cheaper but tbh its mostly snobbery imo, i know where my moneys going when it comes to replace tyres 
but you are right in saying if there are other underlying problems it wont matter what tyres you have the handling problems will still be the same 
Yes I had a feeling you would

Fire away, but don't say you where not warned...

But clearly you 've not tried them on the omega, so impressive confidence levels there:-X
Just to be clear, the worst possible combination is the 912 on a 17" wheel, the 452 is not as bad in that size. Then in the smaller wheel sizes the symptoms are less pronounced again on a 16". So if you must fit falkens fit the 452 to a 16" rim.
Edit, in my case on a 17" rim.....
To begin with they won't feel too bad, in fact when new they are so quiet the it will give the illusion that a massive improvement has been made. But actually the improvement in handling will be only marginally better than the worn put shagged tyres that just came off, so you'll think all is well to start with.
Then after about 4k you'll find the tram lining creeps in, after 7k start looking for faults on the car, after 10k post up on here asking for desperate help as the car is almost impossible to keep in a straight line. Other kind members on here offer to swap wheels having driven it to declare the thing "definitely not right" and " that cars flecking dangerous,I ain't driving that again"...! on a single carriage way the car had a built in speed limit of 50mph as it simply would not stay between the white line and the verge, any faster and the driver could not react quick enough to keep it out of the ditch/on coming traffic.
These tyres are absolutely appalling on the omega and quite easily lead to a dangerous condition. Now if you want to disagree with the facts as laid out and witnessed by two other highly respected admins on here, then be my guest, but be advised, with other wheels shod with two other makes Dunlop where fitted to the front of the car, half the symptoms disappeared. That was enough for me to bin them with another 5k worth of tread still to use in favour of sports contact 3's. From that point on all problems disappeared instantly. It was a delight to drive. But then it would be, new unworn tyres where now fitted with a nice flat profile, they WILL handle better new, but the real proof was that the sc3's never degraded to the level falkens felt like from new.
So fire away as said, fit falkens, just post up on here where and when your driving your car so we can all clear the area. Shite stability, shite grip on the 912 and poor wear to boot. But they are quiet
