Is the higher the kelvin # the brighter the light?
In perceived light in some fluorescent bulbs, it CAN mean this, but it certainly does not always mean this. Again, perceived light, not necessarily the actual light output. It is dependent upon the actual fluorescent bulb, and since it's nearly impossible to track down accurate S/P ratios, it's pretty meaningless. For all intensive purposes, yes, higher kelvin is a brighter
perceived light.
But since I don't know of many "super bright " 6500k fluorescent lamps (though they can have extremely good CRI, so to answer your question, the higher CRI at 6500k appears to lower lumens, but there isn't a specific correlation, probably just lower demand for a 6500k high cri bulb), I'll throw out some suggestions for 5000k.
Ushio 800 series
Philips 850 series or Alto/plus
Litetronics also makes an F32t8 that is supposed to be extremely bright, but I haven't used them.
FWIW, you aren't going to find much "brighter" than 3100ish lumens, right around what you already have. You should probably be looking for the highest rated lumen FULL SPECTRUM F32T8.