This is very belated, but I found this in a related search, and figure others will find this in the future looking for the answer to the last unanswered question, which question still holds relevance.
While the owner of 4sevens on CPF called using [higher-voltage] rechargeables in the quark mini's "crazy", I've had no problem, and I disagree that it's crazy on short runtimes. Same LED and voltage as you'd have in any other flashlight, just lower maximum output the battery can easily do (same chemistry and voltage though), and less heatsinking ability. But plenty of crappy bigger LED lights out there come with essentially "no" heatsinking. 4sevens paid attention to heatsinking and that is their main concern when they warn you away, assuming someone out there is gonna let a batt bleed out on high. I also like that the Quark MiNi starts on Low, so even if it did turn on in your pocket, there's no reasonable chance it'd get to High.
At first I bought a pair of "3.0V" (they are really LiFePO4) on dealextreme for cheap--I believe the ones linked above. While not approved for that type of battery, I used my much-loved "universal" charger with a few DX mini rare earth magnets to make them fit. It overcharged them to 3.8V instead of the recommended 3.6V top end, but they worked.
I knew the light could have more output. I finally located a true 4.2V li-ion (LiCo) cell from LightHound. It did produce more light output. I was finally satisfied. I usually use the MiNi on low or medium anyway, and only use High for short bursts when needed. The Lighthound blue unbranded cell is unprotected an IMO does not need to be protected. It is labeled as a 15266, 300mAH, current price $4.55. This is the only 4.2V CR2-sized cell I know of, but luckily, it was the last one I needed. No problems. Even considering I only use it normally seconds at a time, the battery lasts surprisingly long. After maybe 6 months, it's down to 3.6V, and I charge it.
http://www.lighthound.com/RCR2-Unprotected-Rechargeable-Lithium-Battery_p_1577.html
I got my MiNi for quick things like fumbling with keys, checking the mailbox, and doing a quick checking of the engine compartment for funny noises (where the high available power of the Li-Ion comes in handy). I try to have a bigger flashlight around, not for more light but simply runtime if needed. I started out with the idea to carry a P60 host in my carry bag and in each car if I forgot, but I'm finding an SK68 with a 14500 works satisfyingly well, is handily smaller, and AA primaries as emergency glove-box backups are cheap easy safe and better at handling car heat than Li-Ion.
I use my trusty (much-maligned at CPF) "Universal Chargers" also for the 15266. Like these (Manafont has 2 at different prices which look similar or identical):
$3.78 HUANGAO - Single Lithium Battery Charger for 1.2/3.6/9V Battery(100V~240V)
$4.79 Universal Smart Quick Charger(100~240VAC)
Very slow charger, which I like, good for small cells especially. All mine slightly undercharge at under 4.20V but over 4.10V, which is safe and good for battery longevity. Takes all night to charge an 18650 from 3.6V.
Again you'd need a mini-magnet or something to bridge the gap. Lighthound sells a single strong battery for this purpose which I got, and it works fine,
Magnetic Spacer for Charging CR2 or 14250 Battery ($0.95)
but so does a short stack of narrow neo's from DX.