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A quick look on the internet reveals stainless steel has a higher electrical resistance.
Cooper for example has a resistivity of 1.68×10−8
Aluminium 2.65×10−8
carbon steel 1.43×10−7 (note the minus 7 not minus 8)
stainless steel 6.90×10−7 (note the minus 7 not minus 8)

So i can easily imagine copper is the most desirable choice. That said is Stainless steel still a problem? should i just make them slightly larger to compensate?
Sure. Just make them 69/1.68 = 41 times as high cross section!

Original was 25mmx3mm (75mm2) how much larger would be desirable? 25mmx4mm (100mm2)?
41 x 75 = 3080 mm², say 100 mm x 31 mm. Or to retain the original width, a thickness of 3080 / 25 = 123 mm. You'd need really, really long bolts, and drilling 123 mm stainless steel would be a bitch.

Now you can see why people don't make battery straps out of stainless steel.

I've never even heard of aluminium straps; always copper. Aluminium is brittle.
 
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