It is not that they want me to spend work time on it. They want me to transfer ownership of the project to them. That's the part that I do not wish to do.
The way things work at this place, I'll probably end up maintaining the product until I leave my job.
The reason for not transferring over is that once I do that, they will essentially not let me create features that I think can be done better using my product, because they exist in some other product.
So then the real question is who maintains creative control over the project. But if you're project lead for it , that would be you?
It sounds like there's a lot of "politics" that you're unaware of or not mentioned. Is the project actually in competition with one of your company's products? If they're an open source company, how do they handle community governance and contributions? Do they normally make contributors sign over copyright, like the FSF?
Why do you think there would be conflict over features?
Are you able to fork it? If so, there is then the issue of who gets to keep the name of the project. Also if you fork it, then now you will maintain two versions of the software (until you quit your job at that company), so that is another consideration. (It is also possible that the versions will not diverge right away, but might simply be a copy until there is some disagreement about what to do with it.)
If it's open source, you can transfer ownership to them, fork it, and continue working on your fork on your own time, adding whatever features you want. That would likely piss off your employer, though.
Why not negotiate a VP or Product Manager position out of it and a nice pay rise, maybe even a share of the profits. Let them market it and take the risk, you become the man.
The way things work at this place, I'll probably end up maintaining the product until I leave my job.
The reason for not transferring over is that once I do that, they will essentially not let me create features that I think can be done better using my product, because they exist in some other product.