I've been down this road before and it's an absolute nightmare when you have to work on "obfuscated" code because it drives up costs tremendously trying to debug a problem on the client's server when you, the developer, can't read the code. You wind up with "deobfuscators", copying the "real code" to the client's server or any of a number of other issues which just become a real hassle to maintain.
I understand where you're coming from, but it sounds like management has a problem and they're looking to you to implement a chosen solution rather than figuring out what the correct solution is.
In this case, it sounds like it's really a licensing or contractual issue. Let 'em have the code open source, but make it a part of the license that any changes they submit have to come back to you and be approved. When you push out patches, check the md5 sums of all code and if it doesn't match what's expected, they're in license violation and will be charged accordingly (and it should be a far, far higher rate). (I remember one company which let us have the code open source, but made it clear that if we changed anything, we've "bought" the code for $25,000 and they were no longer responsible for any bug fixes or upgrades unless we bought a new license).