I had tried TWRP through Odin flashable and also Goo Manager. I tried 2.7.0 and 2.7.1, both Tmo and Can version, and none could mount anything . CWM through Rom Manager works great though.
I know, from my experience working on ROM's and getting the first Heimdall flashable package to upgrade the Galaxy S 4G from Wind, that the Wind models of phones are slightly different than the Tmo versions. It took me a dev a while to find the right files, lots of soft bricking ,etc, to figure out the minute difference to allow Heimdall to flash a package, and even then, Heimdall could never flash a modem to the 4G-Wind Variant. I even tried working with the Heimdall dev to find out why, and never could. Modems would flash from CWM or TWRP, but not from the PC, even though Tmo firmwares and ROM's worked, so maybe the Wind phone is slightly different in partition layout that CWM can adapt for, but TWRP can't. Maybe I'll contact the TWRP team and see if I can help them figure out why, although now I'm working a lot more than I was and don't have a lot of time to flash my phone 100 times and brick it and flash again like in the older days.
As far as partition layout goes, all of the T999 and I747 variants are the same. I believe the Sprint and Verizon ones are as well, but am not 100% confident in that. You said you tried the d2can and d2tmo versions, but what about d2lte? Everyone should be just using d2lte now as ALL the S3 models have been consolidated into that one. Where did you download it from btw? You can get it from the link in my sig. I know for sure it works. (I think I still need to add 126.96.36.199 though. But 188.8.131.52 is there.)
I looked in your sig but don't see a D2LTE TWRP, only the 2.7.0 TMO one, which I downloaded from the official TWRP site, as well as 2.7.1 and neither worked. I also tried installing from Goo Manager. Maybe I'll try yours since it is a CWM flashable zip as opposed to an odin tarball and I have CWM working
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