Re: "This means by definition you have to pick things up twice"
I feel that you may be taking that more literally than is intended. I see it as meaning, don't do the same thing more than once. The thing to "pick up" only once is the action, not the physical item.
That is, don't repeat the process of:
"What's this? Oh. Right. Hmm. I should do something about that. But not now. I'm going to put it back on the stack." (ACTION: Decision)
folowed a month later by
"What's this? Oh, that thing again. Eh. I'm going to put it back on the stack." (ACTION: Decision)
followed a month later by
"Oh, my God, this again?! I don't know, all right? Back in the stack with you." (ACTION: Decision)
Instead, the process should look more like:
"What's this? Oh. Right. I should read this, but it's not realistic to expect to do it this month. I'm going to file it under its title, and add a line to my 'To Read' list that will allow me to find it when I get to that line in the list." (ACTION: Decision)
followed an hour later, at the file cabinet, by:
"OK, that's filed." (ACTION: Filing.)
followed a month later, when reading the To Read list, by:
"Oh, yeah, I remember that. Filed under Blah...got it. I'm going to take it with me and read it at lunch." (ACTION: Task selection and un-filing)
followed twenty minutes later by,
"All righty, got my sandwich, now let's read this thing." (ACTION: Reading)
So you handle the physical object multiple times, but the action is different every time.
As for where to put it, I'm working on this decision right now, in yet another tweak of my system. I'm trying to move more and more and more things out of my active projects and lists, as I learn more about my (low) tolerance for long action lists.
I try to have a very clear line between my active project and action lists, and anything and everything that I can get OUT of my active project and action lists. So while someone else might have a "Reading" project with sixteen actions in it, I'll have a "To Read" list with sixteen items in it, and a single action, "Review To Read list and pick something" in my action lists. There's no real difference between the two, except a psychological difference, for me, in having shorter 'action' lists. Similarly, where someone else might brainstorm a bunch of possible actions for a project and leave them in their actions, I will store that as project support material, somewhere else.
But where? Physical files? Notebooks? OmniOutliner outlines? Text files? Digital files organized by a database? Where? Where? Where?
I'm leaning toward "Digital files organized by a database" but that may just be because that gives me the pleasure of either shopping for or writing the organizing software.
Oh--the one "where" that I am satisfied with is "where" to store incoming emails that serve as support material for actions. Those, I store in a big email folder of all emails for the year, and the action has enough information to find the relative email. ("See email from JSmith 5/5/2010") The success of this method is why I think I want the digital-files-stored-by-database scheme, because I could do a similar thing. ("See garden diagram labelled '150510 Veg Revamp'") There would still be a modest amount of paper, but I think that would be rare enough that I could come up with a scheme that works item by item.