Lib_deps creating different versions of included file?

You should create real libraries, not just header files.
Then use lib_deps in combination of symlinks to point to those libraries from different projects.

See Creating a library
See Local folder

If you use a file structure like this:

.
├── libraries
│   ├── LibA
│   │   ├── src
│   │   │   ├── LibA.cpp
│   │   │   └── LibA.h
│   │   └── library.json
│   ├── LibB
│   └── LibC
└── projects
    ├── ProjectA
    │   ├── include
    │   ├── lib
    │   ├── src
    │   │   └── main.cpp
    │   ├── test
    │   └── platformio.ini
    ├── ProjectB
    ├── ProjectC
    └── ProjectD

You can reference your libraries from the projects by

lib_deps =
  symlink://../../libraries/LibA