As a few people have suggested, you really may just need 1-2 months of riding this bike to get used to how it feels and handles. Give it time and try not to get discouraged yet. It looks like a great bike and your position looks quite reasonable. A road bike like this is supposed to handle very differently from what you've been riding. It is supposed to handle nimbly. But before you get used to it, that translates into squirrely. After you get used to it, it feels stable but quick. Once you get to the point where the bike feels stable and you can handle it with confidence, then you may still have to tweak your riding position.
P.S. In a previous post I mentioned headset adjustment. If that is off it will affect the steering and needs to be fixed. Did the LBS ride the bike after replacing the fork? Do you have an experience road-biker friend who would give it a spin to make sure the bike is riding properly?
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72