Git-LFS is made specifically for that very situation. Unfortunately it
is also developed by Github... so the client is open, the specification
is open, but the server is closed (so they can charge you to use it).
There's some open source server implementations but I don't know how
good they are.
If all the files truly are read-only, then putting them in git should be
okay. There's a couple downsides that I'm aware of: First, they will
always be in the repo, so even if you "clean" them out they're still
taking up disk space (unless you descend into the guts of git to excise
them). Second, checking in a very large file (100's of MB) can take a
long time (several minutes per file).
It sounds like what you really want is a content management system,
which is a bit of a different beast from Gitit.
Simon