Before going down the technical path you suggest, I first want the higher level question answered; that being, will "TestComplete, with TortioseGit, will work fine with a repo having the Git Large File Support (LFS) extension"?
That there is no mention of LFS in the TestComplete documentation makes me wary and cautious about starting on a path that may be a dead-end. This is especially true given the TortioiseGit does support LFS as evidenced by this article:
https://tortoisegit.org/docs/tortoisegit/tgit-dug-lfslocking.html
Champion Level 3The TortoiseGit Client bundled with TestComplete should support Git LFS, provided that Git LFS is installed and properly configured on the system. Since TortoiseGit is a third-party tool, TestComplete documentation typically only covers its own functionality and limitations of bundled components, but not all capabilities.
You should be able to quickly test to see if TortoiseGit Client LFS works.
