A more common frustration with first party cookies is that you have to choose what domain the FPC lives on.
If you have two domains each with their own report suite, and a global report suite capturing data from both, how do you decide where to put the FPC?
If you ask me, there should be an option to have a mixed cookie setting: both a 1st and 3rd party cookie set with the visitorID.
In concept, the idea works as such:
Visitor lands on a.com (FPC and 3PC are set with the same visitorID) and data is sent to a.com report suite and global report suite
Visitor lands on b.com the next day (3PC is read, FPC is set with same visitorID) and data is sent to b.com report suite and global report suite
Obviously, if the visitor is not accepting 3PC's, there's nothing we can do and the visitor is not de-duped in the global report suite.
Sounds cool, eh?
Similar idea here http://ideas.omniture.com/t5/Adobe-Idea-Exchange-for-Omniture/Allow-for-the-use-of-1st-par ty-Cookies-on-Primary-Server-Calls/idi-p/7283
Think your approach is probably better.