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Now reading more about it the current might be coated Cordura but they started by using truck tarpaulin.
As for welding, it might be possible but quite hard on a complex shape. I did a mudflap from tarpaulin and welded 2 straight edges using the heat strip on a vacuum sealer. It was messy, kept sticking to the strip and needed about 10 passes to get through.
Some people use modified soldering irons.Cool article about Ortlieb, what they use is called high frequency welding.
https://bikepacking.com/plog/inside-ortlieb/
Maybe you're right, a had the roller classic plus in mind when I wrote that which are a slightly different material to the regular.