You're on the right track -- two things:
1. 2 stops is a lot of underexposure.
2. Watch the terminology here. Normally I prefer not to nitpick at folks over the right words etc.. But in this case how you put it into words can really influence what your doing. It's not fill flash if the flash is the dominant light source. You're talking about taking a flash photo and including some ambient exposure. When you're using fill flash the ambient light is the exposure source and the fill comes in under that to soften the shadows. What you're describing is entirely different -- you're taking a flash photo. Exposure is determined by the flash and you need to know that value and make sure you know how the ambient light compares. At a given ISO: flash exposure is a function of f/stop, flash power and flash to subject distance while the ambient light exposure is a function of f/stop and shutter speed.
Joe
Yeah, it's fill in flash since that's all I do these days - taking pictures under the harsh day light.

I also recently got a 3-stops ND filter, hopefully this will help with the DOF a bit too.
Flash filling not too long ago...