O have successfully soldered wires to aluminum foil but nothing as large as the joint you are trying to make.. In my experience, the key is to be able to remove the oxide layer on the aluminum and get down to the bare metal. Actually, the same is true for copper. If you have a black oxide layer on the copper, it is impossible to solder. The difference between the two is that the copper oxide can be dissolved with an appropriate flux while the the aluminum oxide has to be removed by mechanical means. Also, aluminum oxides very quickly in air.
If you can manage to tin the mating surfaces, you should be good to go. Once tinned, the solder will flow into the joint.
Something that I haven't tried but might work is to use an inert atmosphere to prevent the aluminum from oxidizing. I am thinking of something like a small glove box and argon gas. There are also available zinc based brazing rods which will bond to aluminum. again, if you can manage to tin the aluminum with it, you should be able to solder that surface.