I really don´t think you have to quench unless it is specifically asked for.
If I had any saying I would ask you to grind down what you have done, tag some square bar to both long sides, start your welds there and cut them off later.
you could even bevel the sides a bit before you tag the sacrificial bar to it since the corners are what takes the most stress.
I would travel the short distance, place one bead half on the other not at random spots. Lay some square lines with soap stone to keep the welds square to the anvil.
Keep it clean, preheat and go hotter