Really like these, but I think it may be giving a electronics (as in hardware) feeling. I think you should shift focus away from the Electronic part of EDI and more on the Data or Interchange part of it.
Also very important: we need to be able to place whichever logo (or portion of logo) into a squared desktop or application icon. Can you help us out in imagining what that would look like?
I sampled the colors from the image link you provided. If anything still looks off, tell me what color you would like adjusted or send me the hexidecimal code colors for Astera. I logos #86 and #87 show both the full logo and the corresponding desktop icon. #85 is simpler and does not have the glossy overlays.