You only need to synco the carbs if you have separated them or messed with the synco adjuster. As far as jetting a high flow filter will definately lean out the bike. If you install a jet kit the instructions will tell you to lower the clip two position vesus a stock filter.
On most modern bikes with tuned airboxes a stock filter is recommended, an aftermarket unit actually reduces power on a stock bike. It sounds like you're stuck with it so that being said buy a stage 1 jet kit and follow the baseline jetting instructions for a stock bike with high flow filter with regard to your altitude. If you want to go really cheap you could shim the needles and maybe richen the main jets.