Hey you guys,
I don't know about your machines, but my Technics gets an almost perfect tape pack when I rewind a tape. It's also a constant tension machine so it should be fine to store the tapes for a little while this way. I do it all the time when I'm using a particular tape for tuning my system(tube rolling, trying cables etc). Even if there are a few wraps that are a little uneven and sticking out just a bit, it shouldn't be any problem. You do need to be a little bit more careful not to expose the tape to temps that are much above 68 deg. F (20 C).
For others reading this thread, bear in mind that I know that Doc or Shawn have adjusted both of these machines in question and so I'm sure that the tension is correctly adjusted. With other machines I can't be sure and more caution should be followed.
If the tension is adjusted too high and the tape is unevenly wrapped, then there's the danger of cupping the tape. One of the forces exerted upon a spooled tape is toward the hub of the reel. And if there is enough of the tape edges sticking out of the wrap and thusly, unsupported by the preceding wraps, the edge will start to bend toward the center. If you leave a tape like this for too long, this bending will become permanent and this "cupping" will result in decreased tape/head contact and lowered output of that channel.
If you'd like to know more about these kinds of tape problems and precautions you should take to avoid them, check out the "Tape Basics" section of the Beginners Guide which in a sticky about the General forum.
BTW Xavier, did you have any luck with your vibrating reels?