In hindsight, I also made some mistakes in how I went about evangelizing it.
It sounds like the author implied the company actually had something to do with whatever it is. That definitely makes it an unsanctioned overtime project rather than something separate like a side project.
I don't think it really applies to the side-project rights case, but there's reasons to control overtime and require permission for it: Trying to ensure lower management/peer/customer pressure don't cause people to overwork themselves, if people work more on additional projects they're not asked to do they might be less effective at the main work, in some places (probably not the US) it's a legal risk. My employer in Germany has such rules, although I'm not sure how strictly they're enforced.
Sadly, for programmers in the US, overtime is essentially always unpaid. When you e.g. hear about game developers doing 80hr/week crunch time, they're not getting paid extra for that.
I get that, but 'unsanctioned overtime' sounds as if the company was robbed of something. Since they never paid for that 'overtime', how did it need to be sanctioned?
Going that route, maybe the company could pay for the work done on the project.
If the company really want to act in good faith, as reading between the line I assume you believe they do, they would have opened with an offer or some sort of compensation.
Instead they flat out asking you to transfer your work over means they knew and has already calculated the consequences.
Sorry to be cynical, as others have point out go and talk to a lawyer.
My number 1 rule when it comes to side projects is to never create something closely related to my employer's business.
As an employee, if you put a lot of your business and technical knowledge (that was acquired while on the job) on a large side project effort without your employer's consent, you're playing with fire, because you may be transferring business advantage from your employer to the outside world, including the competition. You put yourself in a position where you could even get sued if things go badly (specially if your project is a potential money maker)... See the case of the Nginx author, who just got himself into similar trouble...
In conclusion, I think your safest bet is to, as everyone is saying, talk to a lawyer... not to threaten the company, but to protect yourself and hopefully come to a friendly agreement at the end!
As much as I hate to say it, that doesn't sound like a side project. That just sounds like overtime.