Takeshimiya, this helped a lot, thank you
Hard to believe I've been using tar wrong ever since, lol. Funny enough, it works on Linux just the way I expected it to.
It is almost perfect now like this:
export repo to %SYSTEMTEMP%/SomeTempFolder
cd to desired location of archive
tar -cf archivename.tar -C %SYSTEMTEMP%/SomeTempFolder .
The only issue that remains is that tar puts everything into a folder "." inside the tar archive which is a little unpleasing. Luckily, this does not matter much, as the archives unpack fine. Sure one could work around that, but I guess I'll leave it. None of the compression utilities that I have tried seems to have a problem with it.