I know they [used to] make a quick connect cable end for TV cables. It was just a smooth, springy plug - a lot like an RCA jack, but fit the profile of the TV cable. Anyhow, I don't see why a similar idea wouldn't work. Then you can stick the battery in at whatever rotation you prefer. Of course, the problem then is that it's not as stable, and can spin freely with just a bit of torque.
Spring idea is sound too. Attach bottom of battery connector to a nut on a post with a spring. Push down and twist to rotate the battery 1/6 to 5/6 of a rotation from its natural resting place once attached. Wouldn't be a problem as you don't have to shove down on the battery when attaching it, just twist.
Final thought - more like the first. How about a clamp? Like the quick-release type on a spring form pan. You stick the battery in and then lock it in place. The latch could be flush-mounted with just a tiny piece for a finger/fingernail to get inside for changing battery. It would *sort of* be like the battery cover on a remote in that regard.
You'd also have to place the atty adapter far away enough that you could use different tanks - and some of those are wide. How about instead of perfectly parallel, you consider attaching the atty at a slight angle away from the battery - say maybe 10-15 degrees or so. It would allow a smaller footprint for the product itself (not including battery and atty), and give the assembled product a little more width. More width equates to more stability in your pocket IMO. Also, such an angle would reduce or eliminate the problem of almost all atty/tank deals being shorter than almost all eGo-style batteries because it would move your lips away from the base of the battery.
Alternatively, another solution for that is to have the atty side connected to a large bolt screwed into the base of the product. If the overall height of the "base" was, say, one inch (random measurement), by unscrewing this bolt to the desired length, the atty could be extended by close to an inch. Again, there are alternatives to the solution, like using some kind of locking rod in lieu of a big, hollow bolt.
There are a lot of potential neat solutions to these problems, and it's a nifty idea. You can use whatever battery you want and maintain a form factor you enjoy. Heck, by using a Twist battery, you can save yourself a lot of the cost and/or headache of buying or making your own VV box mod.
After looking at all the great graphics here, I think I really need to learn to do that stuff.