I am a little late with a reply but finally here if you are still interested. Tap storage has always bugged me as an old machinist once told me that to let taps bang against each other was just like allowing reamers to bang against each other. They get chipped and dulled. Good taps are expensive and cheap taps aren't worth having unless you like headaches. So as soon as my Kennedy tool chest set arrived I made this tray to sort my "taps in use". Taper, plug, and bottoming in all popular sizes and taper and bottoming in less used sizes. It is quick and easy to find what you want, and return to storage when finished. They are protected and at a glance you can spot what is NOT there. Never leave the tap in the drill box again. Downside is it is rather large and bulky. I seem to do a great amount of tapping so in my case anyway, the space spent is a good investment. Duplicate taps are separated and stored by size in a little multidrawer storage box.
Slots were cut on the mill with round end mills. After I cut the major length I deepened the cut about 1/4 of the length on the return. This allows me to touch the end of the tap and have the other end pop up for me to grab. Labeling was done with a hand held tape labeler. I cheated, as I started with a piece of prefinished plywood with a wood grain pattern salvaged from a cabinet shop trash can.
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As you can see the tray takes up a little over half the drawer leaving room for tap handles, upper right-pipe dies 1/8" to 1", tap guides, "T" handles, a few ACME square thread taps and a small box of duplicate small taps. Also left in the drawer, but not shown, are several different charts and slip sticks showing recommended drill and clearance hole sizes. I always tried to keep it simple for my guys, so when screw-ups happened there were less excuses.