Of course you are using a variable resistor, so infinite control and longer runtime.
What potentiometer are you using? Jameco has some that might work, cheaply (would any of
these work?). I was a big fan of the instant gratification, Radio Shack $3 25 ohm (if I recall correctly) variable (modifying direct drive and china controller that are not fixed current), until I got addicted to the Buckpuck with its dimmer (ledsupply and other sources).
Undoubtedly, logically, the way to go for sub $10 low-lumen lights is: 2 AA + cheap electronics + removable tir (dirt cheap and swappable beam patterns) + highly efficient & accesible led, but not over priced. Though my xte was white with no optic, but wanko colors with reflector, never tested with tir.
My daughters hang onto lights fairly well, maybe a loss every 6 months. Wife and son can loose one or two light a week. Price matters.