Since you seem pretty attached to using your thin sheet metal, there is a possibility you can try. Make a series of U channels with your .5 mm sheet, each channel the same length and about the same height, but with gradually decreasing width. Stack them together, and weld the areas in contact.
simulate this circuit – Schematic created using CircuitLab
This figure shows the idea in cross-section.
If you use, let's say, 10 pieces of aluminmum, the maximum base thickness will be 5 mm. If you can produce small differences in width you can produce a lot of fin area for a given overall width.
There are a couple of problems you need to think about.
1 - You must keep the bottom of each channel absolutely flat during welding, or the finished heatsink will not have a flat base, and you will not be able to make good thermal contact with your Peltiers. This probably means you will need a spot welder, rather than an arc or gas welder, and will require real attention to what you are doing.
2 - Because each channel is connected to the others at separate points, the thermal conductivity of your final base will be less than if you made it out of solid aluminum. It may not be too bad, though, since each sheet is pressed against its neighbors.