Diagram b is the way to do it. Put a tack on each corner first so you have something to weld into.
I didnt want to get into a debate about stick, mig, gasless and tig welding as all have advantages and disadvantages.
I have all these machines and if i were doing your project i would mig it without a doubt. Mig welding is the easiest to control.
Dont go using pub bottles of co2 as this gas reacts with the weld pool and increases penetration. Its actually called mag welding, the i in mig stands for 'inert gas' and the a in mag is ' active gas'
I have used pure co2 many times on thick sections – above 15mm thick for ultimate strength after preheat. It is hard on your torch and consumables, produces alot of spatter and gets really hot.
As a solution to your immediate problem would you want help / allow someone else to do it for you?
I have a small gasless mig welder that could be chucked into the car and brought over to you. I also have a a pair of hands available, and a welding mask… I am not trying to muscle in on your project but the offer is there.
The gasless mig is a bit harsh but i am confident it will do the job. After a bit of clean up it will be ok.
I would bring the mig and a bottle but its big and very heavy.