Both で and から work fine. Using で twice itself does not look odd to me because these two で clearly serve different functions. But in this case から may be a bit easier to understand because it's more explicit about what turns into what. Another simple way to say this is 合繊を生地に織りあげます. Many compound verbs in the form of ～あげる take
AをBに and add the meaning of "putting A into B" (e.g, 鍛えあげる, まとめあげる, おだてあげる, 仕立てあげる).
What I'm more concerned with is the mixture of casual and technical words. 織機 is a difficult and technical term, while 超速 is a highly casual and/or manga-like word. If you want to put this sentence rather seriously, you should use 高速で ("high speed") or 超高速で ("super-high speed") instead. 合繊 also looks jargon-like to me, so you might want to replace it with 合成繊維 depending on the audience of this sentence.