Having a non-standard size is exactly the reason the tab character (not the key) is unusable. If you accidentally get some space indenting anywhere in the same project as tabs, then it'll be misaligned on someone's editor and they'll "fix" it, making it misaligned on someone else's. Trying to never use space indenting is impossible. Never copy and paste from anywhere else, never manually align multi-line statements, never align comments with code, etc.
IMHO, issues with formating, like the ones you describe, should be cought by a linter. Or even better yet, enforce format-on-save in all editors your team uses and have it automatically re-indent and reformat the code so what indentation it was originally indented with irrelevant. I think this approach would work, but I tend to work on files < 10k LoC, it might get annoyingly slow past that.