Get into the corporate mindset and attack from within with something finite and low risk. Whether it's your direct management, or further up the food chain, there's someone somewhere worrying about money and schedule, and if you can sell your idea on money and schedule, you're likely to have a lot of success.
This is the general process I've seen be successful:
- Start from experience - pick 1-2 (at most!) open source products that would be strongly beneficial to a project you're working on. Ideally, this is a new project, or new big feature in a big project, that can be segmented to avoid lots of rework. Pick open source products that are very mature with long records of successful adoption on big products. Even better if the open source shows a longer life than a competitive 3rd party product.
- Do estimates - how much work is open source likely to save over alternate solutions? Get some numbers in manhours and also a sense of schedule. Also get numbers for how often new releases are delivered by the open source community. It might also help to know how many bugs are fixed in each release (especially if the bug fix is trailing off, which suggests maturity), and how frequenty interfaces are deprecated - since management may be afraid that the project will be dependant on something where you are forced to rework frequently and heavily.
- Get the legal stuff - grab a copy of the licenses. If you can, get a friendly consult with someone in legal. Having the legal department on your side is a big deal here. If they agree you are safe, your management is a lot more likely to be OK with this.
- Have a backup plan - Research options for the open source version of "tech support" - both the free community sites available and also the costs of hiring an expert consultant, if things shoudl go really bad. Generally, I think a case can be made that an open source consultant can actually be cheaper than a maintenance contract for a 3rd party product. And it's good to know that in the event of emergency, there is a "throw money at it" potential answer.
All that data put together spells maturity. It's a strong case today that open source projects are as big, stable, and reliable as a solid 3rd party vendor with a good track record. But your management won't get it if they don't see the data for themselves.
A good place to start is a small, wacky project with a small budget and little financial risk. That's another reason to start small. With 1-2 carefully chosen open source components, you have a shot at getting management to dip a toe in the water. If they are deluged with 20 open source requests, they may be likely to clam up in terror.