Beorean: If you're not accosted, find a side door that you can prop open. Tape on the latch or a stick would do the trick. Be obvious when leaving. Now, you can return Saturday night after midnight. Take a large duffle bag, a flashlight, bolt cutters, and at least 12 small lock. Now, when you break the locks, remove all of the contents in the cabinets, and re-lock it with a good lock. That way, when the next brother walks by the cabinets they'll be locked as usual. Nothing suspicious.
Finally Beorean! I was thinking I had the only criminal mind here. I have wanted to do excactly as you said for quite awhile, or hide inside till all are gone. However, at my hall an exit door is right beside the file cabinets. So you can back up behind the hall and with a hand truck take the cabinets with you in about 45 seconds by pickup or van. I would NEVER conceal the theft at all, I want them to be shook up! There is soooo much crap in those files. So many cases result in nothing or private counsel, esp. the "supposed" child molestation stuff (I mean to the elders it is "supposed").
I would be the first one in the parking lot at the next meeting just to see and hear the elders.....oompa...i guess if you wanted to be cruel you could just copy the crap you want and post it on the bulliten board or leave it lying around at will.