When I had my Omega (2003 2.6CDX) I was doing 6.5 miles each way to work. Mine was blowing out some heat within a mile and good heat within 2 miles. That is starting on 30mph road forfirst mile and then 40mph road for next 3 miles and then then 30mph for the rest.
I to removed the filler neck as it suffered from mayo, best thing I ever did for free.
Now mum has the car and does a max of 2 mile journeys in it and she is not suffering any problems like you are describing. We have had the scuttle leak on to the passenger side coil pack and replaced that and sealed scuttle (fingers crossed)
Not wishing to be funny or anything and I am sure you would have noticed but is the thermostat stuck open or partially open ?
I am having a similar heating problem on my Astra where it won't warm up in the 6.5 miles to work. Took wifes Astra and that was warm within 2 miles. I have not looked at my car yet, and weather to cold, but my first port of call was going to be thermostat.