> If I understand you correctly, I should be shooting in Aperature Priority mode with an appropriate f-stop and about +1 correction dialed in.
More or less right. Aperture priority should be fine assuming the camera doesn't let the shutter speed drop below the synch speed when you're using flash. Most don't.
As for correction, experiment. Shoot one without correction, one with +1/2 or so and one at +1; perhaps when you have the film printed you could ask the lab techs to tell you which of the three exposures was best. The main thing to remember is that negative film loves more exposure, the more the better (to a point of course), while underexposure kills it.
> The exact f-stop chosen will probably be determined by some experimentation.
Right. Your camera should provide you some feedback regarding that in the form of some sort of in-viewfinder "flash OK" indicator. If you don't get the OK indication then you'll need to use a wider aperture.
BTW, I assume you've eliminated printing variables as the cause of the problem. Modern machine prints can be superb or horrible; it all depends on the operator.