Throwing away old history on git repo full of binaries

You can rebase the whole show down into a single commit.

Something like

git rebase -i [some early commit]

and then using visual block mode in vim to squash nearly all of them would be easiest, followed by an fsck and gc run.

Alternately, you can use git filter-branch to remove the commits from the tree entirely.

This is one (other) way:

git fast-export master~5..master | (cd ../newrepo.git && git init . && git fast-import && git checkout)

The above example will take commits in range master~5..master and create new repo out of that. You can use the same repo too, but the above will be safer.