Supercapacitor with a rated voltage value greater than 2.7V feasible?
Super Capacitors are a sort of cross between electrolytic capacitors and batteries.

see wikipedia article

Unlike in electrolytics, where you can build the insulating film up to an arbitrary thickness by applying a high voltage, in supercaps the insulating film has more to do with the polarisation layer of a battery, so has a hard upper voltage limit.

The lifetime of the system is also somewhere between batteries and electrolytics.