At the moment, there's some very strong winds up high. We saw up to 167 knots of tailwind yesterday. Going high may get you into something similar, which should help your flight times. In general though, you'd choose the altitude that gave you the highest TAS, and you'll find that at the 'crossover' altitude.
When climbing, you start the climb at an IAS, and finish at a mach number. As you climb, at a constant IAS, the TAS and mach number will increase. At some point in the climb, the climb IAS will equal the same TAS as your target climb mach number. That's called the crossover. As you go higher from that point, now at a constant mach, both the IAS and TAS reduce.
For an aircraft climbing at 310 kias, into mach .80, the crossover would occur around FL290, which is where I'd expect the low end of the height targets to be. For anything higher to work, there has to be a better wind component.