[folivier]

Welcome. A couple points to consider about propane. Since you're considering adding solar can I assume you might also change the batteries to LiFePO4? You might want to consider an induction cooktop rather than propane. Look at how much battery power they would use while cooking.
A lot of Foretravel guys have replaced their propane/electric fridges with household ones. The consensus is that regardless of size they will use about the same energy, around 120 amphours of battery in 24 hours. Another thing is they added a smaller inverter just to power the new fridge. It uses less power and is always on.
And like Tom said just use the generator for large power usage like the convection oven and possibly stovetop.
Valento, a former Newell and now a Foretravel guy installed a large solar system + LiFePO4 battery system on his coach and I think also has induction cooktop and household fridge. Hopefully he'll pop in for his thoughts.