Pack2,
I think that the situation that you describe is one that best justifies the High Speed Climb.
Consider this, En-Route performance is essentially 3 phases, Climb, Cruise, and Descent. The Climb is far and away the most 'fuel expensive' phase of the flight, and every effort must be made to optimise fuel use per mile in this phase.
This will be particularly so on short sectors, such as you describe, when we have eliminated the cruise phase, and the climb phase remains the most critical in terms of good economics management. It is absolutely true that, for short sectors, the 'slingshot' profile (climb to descent point) is the most efficient. Climbing at best Rate or best Econ speed is at a somewhat shallower angle, thus the apogee of your 'slingshot' profile will be at a lower altitude, but far less fuel in a reduced time to that lower level is the result of the higher speed climb.
You mentioned that some of your colleagues were opting for the lower speed (230 KIAS) climb to allegedly reach higher levels with the tailwinds sooner. At your CAS/Mach changeover height for 280/M0.6 at 19167 feet, TAS at ISA is 370 Kt. At 230 KIAS at the same level, the TAS is 306 Kt, some 64 Kt slower at the same Fuel Flow. Your 'slow flying' colleagues will need to find 64 Kt of Tailwind that you don't have, just to remain equal, I think an unlikely scenario. In the reverse direction, flying into a Headwind, the faster climb wins again, as a given Headwind component has a lesser percentage penalty upon GNM per Unit of Fuel at high speed, than at low speed.
As an afterthought, even long distance operations are optimised by the 'slingshot' profile, that is, climb to optimum level, and then Cruise Climb at the steadily increasing Optimum Altitude until co-inciding with Top of Descent. Infrequently possible due to ATC constraints.
An interesting speed profile, 280 / M 0.60, what type of aircraft is this?
Regards,
Old Smokey