Weatherproof junction/extension box with 8AWG wiring - selection and mounting problem
The problem I see is your wire fill with 4 ea #8 wires counted at 3 cubic inches each you are at 12 without a clamp. I would probably be looking at a double gang bell box.
One thing that regularly has to be done in industrial facilities is modifications to boxes or gutters. I would verify your local AHJ will allow this on residential.
I would cut the back of a bell box out to slide over the existing device box and mount it directly to the wall this will look better and provide the additional space to splice the wires. Since the existing box is proud of the wall a bead of calking across the top or even around that box prior to sliding it over the existing box would make it waterproof.
I have done this with both boxes and gutters coming out of concrete walls and steel plate. Your stucco would be the same as a concrete wall.
Trying to splice heavy wires in two tight a space is how wires get the insulation damaged and end up shorting out on the box or they vibrate through at a later date.