Bo, if the concrete you are fixing it to is stable, than what you have will probably suffice, and a larger plate would not make that much difference.
It is like fixing a Bull Bar to a car, it, the bull bar could handle a bull, but if only fixed to the car by a couple of bolts would be useless and break off at the fist bump.
I think your pier will be fine if the foundation concrete is solid, just go with it, you may be pleasantly surprised.
Once fixed to the concrete, is there anyway of filling the pier with sand, right to the top, this helps with vibrations to settle quickly.
Leon
