We have a "Dumpster" set up under our staff forum (both are obviously set to be viewable only to staff) and instead of "Deleting" the thread, you actually just move the thread to the forum of your choice with no redirect. Then it appears deleted but it's still accessible in your trash/dump forum.
You would need to give the mod access to see the forum, but not the thread content (if you want them to be able to move threads to that forum but not actually see what's in the forum once it's moved).
We have a "Dumpster" set up under our staff forum (both are obviously set to be viewable only to staff) and instead of "Deleting" the thread, you actually just move the thread to the forum of your choice with no redirect. Then it appears deleted but it's still accessible in your trash/dump forum.
You would need to give the mod access to see the forum, but not the thread content (if you want them to be able to move threads to that forum but not actually see what's in the forum once it's moved).
We do the same thing. Sometimes you need to look at what was going on in a 'deleted' thread, so it is useful to keep it around for some time.