[jtfairbank]

One argument that may appeal to management is that your open source codebase becomes a powerful recruiting tool.

Many companies open source non-core code, like UI components designed for their domain or server widgets that can be pulled out into a standalone library. It's unlikely that your company will want to deal with the overhead of many outside contributors, unless it's an open source business model which it seems like it isn't. However, a couple of contributors here or there, or even better, someone who forks the codebase but doesn't cause extra work for you by submitting PRs, is a very strong signal that they'd make a good hire. They're interested, know some of the code already, like what you're working on, etc.

Since hiring is very expensive (costs 10k - 50k to make a single hire), this has real business value and you can use it to sway management.

[jtfairbank]

Also, maybe they don't want to dive right in. Can you take the lead on the open source project for a small component and run that the way you want to for 3 months to show them how it could work? Maybe let each team naturally adopt the open source style if they want to, until a critical mass is hit?