You are wrong, the only change that you can safely say the miners won't accept is changing the proof of work from SHA to something else.
Can this be done in software or is the ASIC hardware wired in a way lets say:
Input 2000 Bytes -->Output SHA(2000Bytes), but if you need 500 bytes more for the additional information, the current ASIC hardware is not capable of doing this?
My knowledge of ASIC hardware is limited but i would say yes, it is.