Well, since we're both DIYers, here's my two cents...
Ditch the charger altogether. The LiIon->USB->LiIon conversion is bound to waste a significant amount of power.
Crack open the gadget whose runtime you want to increase, get at its cell and put a tiny three-terminal switch across the cell output before it gets to the monitoring circuit. To the other pin of the switch attach one of the two wires leading to a suitable connector (I'm in love with JST ones available at DX for this sort of job - they are small, unobtrusive and easy to use). The other wire, you just connect in parallel to the existing cell.
This way you have a gadget that works fine off its own cell, but to which you can connect any other LiIon cell via JST connector, flip the switch and have it use the external cell directly - no power lost in conversion.
This obviously won't do if you don't want an external cell hanging from your device (or in a holder attached somehow to said device); on the other hand, you can attach any LiIon at all - 14500 from a flashlight, prismatic cell from any trashed gadget, big fat LiPo leftover from the RC plane that you nosedived on concrete...
Depending on the device, it might work fine off a 4xNiMH battery too (3xNiMH won't do for a LiIon-powered gadget; it'll think the
cell phone battery is empty almost immediately due to voltage incompatibilities).