Option 3 - You need to stop thinking about this so much.
When in closed-loop mode, within reason the ecu will use the O2 sensor to adjust the fueling to the specified range. Theorhetically*, you can 'adjust' that range, but you only want to do that with the use of an Exhaust Gas Analyzer or some other similiar type of exhaust sniffing equipment.
* - This has not been confirmed, I believe the dude who told me this.
When in open loop mode, the ecu provides fuel based on a table developed by Yamaha which assumes a certain amount of airflow through the engine. So yes, if you change the airflow enough then changing the fueling would be best, or perhaps even necessary.
But does adding slip-ons 'open' up the system increasing airflow? Conventional wisdom around here is 'NO'. Adding slip-ons or a K&N filter does not appreciably change airflow characteristics if any at all. That's not been proven, but is the general consensus. The consensus is that the catalytic converter is the primary restriction in the system.
Folks have modified the airbox with varying results, and there are systems out there that replace the stock header (and cat) that seem to offer slightly more power (airflow) but perhaps at the expense of torque.
Regardless, Yamaha seems to know what they are doing and designed a pretty good system with regards to airflow. Not much you can do to change it or improve on it appreciably imho.
As for the Barbarian Jumper, if you do that your are just SWAGing. Not all FJRs are created the same. Though most FJRs tend to be somewhat lean, how do you know you don't have a rich condition in stock form?
So no, you don't need to do anything regarding fueling just because of adding slip-ons. You may *want* to do something with your fueling if you think your FJR is running excessively lean. Either with, or without slip-ons.
Clear as mud?
Ride more, stress less.
