The fact that there are servers which don't allow users to do the sort of log analysis they need to do is not the fault of Google. Headers are the correct place to put the information.
Not only that, but depending on the way the framework works it could break the page itself. I believe CherryPy's mapping for instance provides GET variables as kwargs to the handler, unless the developer added catch-all handlers it's going to blow up the routing and yield either a 404 or a 500.
2. Modify every analysis software/script.
Simple and easy!
The header is the correct place to put information like this, regardless of whether the deficiencies of the server software.
Care to elaborate on how your Apache configuration is already set up for this?
This is certainly not default/standard behavior.
I have no doubt that this can be done by detecting a header for the prefetch (if there is one!) and using Apache's syntax to mod the log, AND then accounting for this in your analytics scripts ... BUT what I doubt is that this will be a simple task to push to the other 100 million server and analysis instances that I don't control.
Not to mention some of those instances will not be like the rest, and the work required to handled this will be great.
As for me, I happily do not run any public websites other than my personal ones, and in that context I don't much care about analytics, so I'm afraid that I can't show you a good way to do this in Apache. For what it's worth, thought, I think the header for prefetch is "X-Purpose: prefetch" in Safari and Chrome, and "X-Moz: prefetch" (yes, really) for Firefox.