Current limiting; super cap charging a lithium ion battery
The circuit you show is effectively a resistive limiter, which you say you do not want.

You need a switching charger like the LTC1513 which will do what you want:



This won't quite meet you 2.4 A charge current requirement in the form shown above, but you could boost the current capability of the switch to meet the need.
The pulse current from your supercaps will go up as the voltage drops of course, so you may end up needing 10-15 A switch capability.