UPDATE http://jsfiddle.net/musicisair/rsKtp/embedded/result/
Google Analytics sets 4 cookies that will be sent with all requests to that domai
Yes it can be done. You only have to request the __utm.gif with the parameters. The rest of the data is just used for keeping track of the source, session start time and/or previous visits.
You can easily transfer the cookies both ways, so your first approach should work fine.
If your second approach works... not sure. I don't know the ga.js code good enough to estimate wheter that would or would not be easily possible.
There is also a third option, run your own version of ga.js. You are not required to use the Google version.
Can it be done as described above? Yes
Why hasn't it been done?