I have a software prototype that integrates with a product from BigCompany (like really, really big). I predict it would take 6 more months to polish it so that it's of commercial quality. But I'm burned out from working solo and need cash. Ideally I would sell the code to them and possibly make them hire me to work on it more. But how to get them to do this? I'm positive they would take me more seriously after a couple of months of work more, but I don't want to overdo things either - for example selling my project to them before I have any clients simplifies the whole deal.
Let's assume you can get a meeting with Bigcompany (which may not even be possible). And assume that Bigcompany hasn't already thought of your idea.
Put yourself in Bigcompany's position. Someone, out of the blue, brings you a barely functional product that integrates with your software and does something. Do you even care? If the idea seems worthwhile, why not assign a couple of the thousands of software engineers you have to do it yourself? Why would you buy a non-functional (if it's not commercial quality it is non-functional) product from someone?
You essentially have nothing to offer them but an idea and a bad implementation of that idea. That alone would get you kicked out of many companies.
If you want your project to succeed, finish it and get some paying customers. Then you have something to show Bigcompany.
I have been in a similar situation. We had a team of 3 engineers working, some on equity, some on part salary, and we needed something that a so-big-you-heard-of-them company had. We approached them, gave our spiel.
They basically told us that we couldn't possibly have accomplished what we had already accomplished in the time we claimed to. (We had.) Nor could we, with their tech, bring our completed product to market. They didn't quite laugh at us. They just didn't get how slow a big company moves and how fast 3 hungry geeks can move.
About a month later, they announced a product directly competing with ours.
We eventually kicked their *ss in the marketplace, which sometimes felt better than our own success.
The moral is, you gotta be careful.
Your bargaining position is weak. Ultimately it sounds like you can only sell it to them. If it's a big big company, they have a lot lot of software engineers. If one person can do it and it's such a good idea, they can drop 5 engineers on it and have it finished before you do.
When pitching to large companies, you need something with a sale price in the millions. If you can't manage that, you should be pitching to another much smaller company that is more in the range for a buy out.
I'd expect that if you plainly explain that you're out of money or energy, you have no leverage. Perhaps you should get a lawyer to accompany you on any such demos with BigCompany. The lawyer can help you protect information that would reduce your chances of success or reduce the value of any such deal.
Also keep in mind that, while BigCompany may have lots of money, they may be risk-averse. They have a reputation to protect. They may be facing difficulties in the economic downturn. Why should they reward someone they don't know for not quite reaching the finish line?
Apply for an accelerator, like TechStars. It's generally out of the limelight from BigCompany, you get cash and support in building the user base.
BigCompany rarely wants to do the work of building a dev team and user base; that's what they pay you to do when they've bought you out.