I want to modify the index of one (text) file without having to change the working tree file state. Is this possible?
Another take on "changing file in index without altering working dir" is to apply a patch to index only. This is often the way GUI git clients stage only selected lines from a given file.
You start out by (if you want) clearing out the changes from index for that file:
git reset path/to/file
Then extracting the full patch for it
git diff path/to/file > /path/to/tmpfile
Edit the patch file to include only the changes you want to apply, and apply just the edited patch:
git apply --cached /path/to/tmpfile
See:
git help apply