RE: broadhead flight?
There are some true bow tuning experts on this board. But since none of them have answered yet, I will give it a shot. Field tips are much less sensitive to tuning issues than broadheads. Having a broadhead on an arrow is like putting small vanes on the front. If your arrow does not travel perfectly straight during the power stroke (that is, the time it is attached to the string), it will start off course and the vanes will have to correct it, but it takes awhile for the arrow to straighten out. In that first few yards, before correction, your arrow will deviate from where you aimed it when it was on the bow.
In your case, it sounds like your arrow is not level on your rest. In other words, it is pointing slightly downward to begin with. To correct this, I would try raising your rest very slightly, if it is adjustable, until you are hitting the same spot as you field points. If your rest is not adjustable, you will have to lower your nock point, again in very small increments, until you are getting the same impact point.