Heavily used repositories get too big eventually.
However 'too big' doesn't really mean filesize so much these days though.
It's more about the fact that (in this case) too big means consequences such as:
More to load into gui git tools
More to search through with tools such as git grep
(a little known super fast mega-cool tool)
More older results when using search/find in git log
To be honest I would consider just starting completely afresh. Yup, bare repository. So I would do this:
cp your project project_4_28_2913 # So this history is still kept
cd your_project
rm -r .git
git init
This probably wouldn't work for some projects where the requirement is for all history to be kept online in the same repo. However, in practical real world employment I have found that the need to go back more than a day or two to look at older git commits is actually pretty rare and looking at commits that are more than a 1 week or two old only happens a few times a year (say less than 6 for a team of 4).
It's a balance of course and at the end of the day I have found that a clean new repo at some suitable point, with the old repo saved, worked best for me.
This approach is also quick and time is money, so while the other approaches are more fine-grained and precise you always need to factor in how much time you want to spend on these processes as opposed to working on deliverable features that will make your organization money.