I use a portable jump starter battery like the one Bob Frogner mentioned. It is the Husky HSK012HD from Home Depot, about $50. It has a 12 volt 17Ah gel battery in it and it is extremely convenient to use. The cigarette lighter output is nice but limited to 5A, which effectively means you are limited to charging your 4000mAh packs at 1C. (I assume you are using 3S. If it's 4S you will not even be able to charge at 1C without pushing the 5A limit on the cigarette lighter output wiring.) Connecting more directly to the battery, either by bringing out separate leads from inside or by clipping on to the big clamps that are supposed to go onto the battery terminals of the car you are jump starting, will allow you to charge your pack at higher rates or to charge more than one at a time. I clip onto the big connectors, leaving the whole unit intact in case the three year warranty needs to be invoked.
The battery is not quite big enough to meet your requirements for 5-6 charges, though, so you would need a couple of these. Even so, two at $50 each, complete with wall wart chargers, is a reasonably convenient package. And you might find a brand with a bigger battery in it somewhere, so it might be worth checking around. A 12 volt deep cycle AGM battery of, perhaps, 30-45 Ah capacity would be ideal for your use. It is expensive, but it is non-spillable, a lot tougher if mistreated than a gel battery and will tolerate deep discharge. They are easily available from solar energy outfits such as Northern Arizona Wind and Sun at
http://store.solar-electric.com/ or Mr. Solar at
http://www.mrsolar.com/index.php (in the USA) They are a lot safer than car batteries because they won't spill even if damaged and the weight is 25-35 lb. Car batteries tend to be a lot heavier, a real pain for some of us old timers.
I have been investigating batteries a lot for 1660 solar power systems I am responsible for in Argentina. I really like AGM if you can afford them. For highest quality (and, unfortunately, cost) I like the Concorde SunXtender line. The best buy on an AGM battery that might fit your requirements is another brand, the MK 8AU1, 37 Ah, 24 lb., at $81 from Mr. Solar. The next size up in that line, 55Ah, jumps to $147. For $150, I can get the Concorde PVX-490T, 49 Ah, from Northern Arizona Wind and Sun. I would go for the Concorde, but that's my prejudice. Depending on how badly you mistreat these, they should last 5-10 years, so its a long term investment.
Sorry if this is way more than you needed to hear about expensive AGM batteries. They are good, though.
Pete Mazur