I've run a modified turbo sedan to well over 200K, including track time. The turbo at least was reliable.
The question is your price range. For the price of a cheap Omega, you are not going to get a reliable turbo sedan. They can be death by a thousand paper cuts more than even a bad Omega. All of the rubber hoses go brittle due to the higher engine bay temps, manifolds crack, exhaust studs go, and on and on. However, there are several options; Sierra, Audi, Volvo, etc.
You can quickly get to the point where it is cheaper and more enjoyable to have two cheap cars instead of one highly modified one. Do a few things to the Omega, then have another project car more for your individual enjoyment. Trying to run one highly modified jack-of-all-trades can be very expensive and frustrating. By the end, I realised that it was cheaper to buy a fancy and fast new car!
On the subject of drilled airboxes, they are the opposite of a cold air intake and usually reduce real world power. They can give false improvements on the RR if you have the bonnet up or have the fan pointed directly at them.