It should be flat out illegal to claim copyright on employees' work like this (which includes making people sign contracts giving up copyright on their work). If someone does something on their own time, with their own equipment, then they should own it regardless of their employer's business interests. These are employees, not slaves.

Google's stance on this was fairly draconian when I was working there, basically Google's position was that they could be in ANY business at ANY time so that ANY thing you worked on was theirs. On the day I joined, one of the other new hires had a marked up copy of the agreement with some VERY simple wording changes that said basically "wasn't in this business at the time the employee started working on the project" (aka a no retro-active clause) because this individual pointed out quite reasonably that if they were working on something in good faith on their own that wasn't part of Google's business and it turned out to be a really good idea, then Google, based on how the agreement was written, could go back and say "but we're in that business now too and you were working for us so we own your idea."

To which the HR person at the orientation had said, "Don't worry Google wouldn't do that." And this individual said, "I'm sure they wouldn't, that's why it seems like a no-brainer to put it into the agreement, it just says they won't do something that you and I both agree they would never do. I can't sign the document as written without this." The HR person took the updated version off to someone (presumably legal). And then after lunch this person was not in the group (I had seen them eating lunch) So when we had finished up, before my mentor had arrived I went out and found them waiting on the circle for a ride and asked them what happened. They said, "Google said no and also said they were rescinding the offer of employment."

And that told me everything I needed to know about how Google really thought about things vs what they said they thought about things.

I think a good strategy is to change companies often and ensure that your side project isn't related to any of them. This creates a lot of complications and adds a layer of protection because if your current employer tried to claim the software as theirs, your previous 3 employers would all have claims (weak claims, that is).

If the software is different from what all 4 companies would produce and it is all built outside of business hours, it gives you full leverage.

If any specific company tries to imply that their claim is valid, they cannot do this without validating the claims of 3 other companies... Thus preventing themselves from obtaining the full ownership rights over the product.

The company which actually wants your software would be better off just paying you and accepting your simple version of reality than trying to create complications for themselves by inventing some elaborate legal fiction.