I would think that your problem has nothing to do with the idle speed. 1400RPM is ok for the bike. If it is not staying stable and dropping off to 1000RPM then shutting off, then there is a different problem. Could be the ECU, a vacuum leak, torn intake boot or the intake boot is not sealed to the head, or the throttle position sensor is not adjusted properly like the 2009 bikes, witch had the identical problem (the fix for the 2009 was to adjust the throttle position sensor on all 650cc FI models). But I would not say the tip-over switch, the bike would not have an unstable idle, it would just shut off ( the tip over switch is the same as the engine shut off switch, its on or off). I also would not say that it is the fuel pump because it would have running issues at all rpms regardless of the temp of the bike, and it sounds like the bike runs good until it gets hot.
I have not seen the new fuel injection, and was very upset when they changed it (Hyo got a long letter from me about that). This system is based off of the Daewoo car, which obviously has never been used on a motorcycle.
My Questions for you would be...
Do you get any FI warning lights? Does your dealer have the HYO hand held computer for the 2010 bikes? If so, is your bike logging any fault codes? If you want to raise the idle it may have to be raised by the hand held computer only (that is how Honda's work, we have 2 CBR600 in our shop right now with very high idles and we can not do anything about it).