Multiple backlogs to file against

so you have iterations like this
Timeline
Product  (not in any year cycle)

Year 1

quarter 1

sprint q1-s1

sprint q1-s2

sprint q1-s3

quarter 2

sprint q2-s1

sprint q2-s2

sprint q2-s3

Year 2

and then you have Plans for each
for Product - Product backlog
for year 1 - Release backlog
for quarter 1 plan  - Release Backlog
for q1-s1 you have a sprint backlog (execution items selected)
for q1-s2 the same
for q1-s3 the same
for quarter 2 plan  - Release Backlog
for q2-s1 you have a sprint backlog (execution items selected)
for q2-s2 the same
for q2-s3 the same

so to move workitems from one iteration to another  you change their Iteration Planned
move from q1-s2 to q2-s1, change the iteration planned. as there is a plan over each,  this should move them
as appropriate q1 is a release backlog plan
etc.

so you have plans that cover each iteration.

now, the easiest way is to use eclipse, cause you can do a couple hundred at once.
create a query that shows workitems by iteration, and pick just the iteration of concern. (note that if you have multiple 'plans' covering the same iteration this gets harder. )
edit the query results to show the workitem Iteration Planned attribute

then select all the workitems you want to move,  right click on the Iteration planned column of the query results panel, and select change Planned Iteration, then select the new iteration from the list presented..
if you have multiple plans per iteration time period, this is ok, I think as you said 'backlog', which is outside those..

but if you  meant to one of the overlapping plans in the same iteration by team, then you will have to use drag/drop in eclipse to make that work, OR once the iteration is changed, also change the category/filed against, which is the TEAM (people) owner.  (which matches your plan definitions, work(items), over time(iteration) by people (team))

I think you'd need to changed Planned For attribute.   Using the RTC client it is possible to do bulk changes on work item attributes (if you have the authority )

Hm.. I posted an answer here but it doesn't show.

You need an iteration labeled as  the appropriate backlog,
then run a query that shows the Iteration planned column (I am using Eclipse for this).

select the workitems to move, right click on the iteration planned column, and select Change Iteration Planned,
pick the iteration with the backlog as its container.

You will want to model a "backlog" as an iteration, not as a category.   So if you want an extra backlog, create a new iteration.   Then to assign a work item to a different backlog, change the "planned for" field of the work item to the iteration for that backlog.  

To bulk move a set of work items from one backlog to another, one approach is to open up a plan for the old backlog (a plan whose iteration is set to be the iteration of the old backlog), multi-select the work items you want to move to the new backlog, and change their planned-for property to be the iteration of the new backlog.