First, the 101.27440 is a 12x36, not a 6. If you lived in the UK or in the Commonwealth, you would call it a 6", but in the US it's called a 12".
The gear driven by the 16T/32T gear on the tumbler pivot should be a 40T and is called the Sliding Gear. The only time that you normally move it from the OUT to the IN position is when you are cutting 4 tpi to 7.5 tpi threads. Which is probably never. The input gear to the QCGB is actually two 48T gears mounted on a common keyed bushing. You can get the gears, the keyed bushing, the shoulder bushing that the keyed bushing runs on, and the mounting bolt, nut and washer from Clausing. Or you may be able to find them used on eBay
Unfortunately, (a) the 3-jaw chucks (except for those more expensive ones that came with 2-piece jaws) originally came with six jaws. Three are used for mounting smaller parts and three for larger. And they are not interchangable between any two chucks. You might get lucky and find four jaws that will actually fit your chuck. But almost certainly the runout will be terrible. So bite the bullet and resign yourself to buying another chuck.. It is possible to re-grind jaws to fit. But it takes a tool post grinder and even with that, you can't do it the way that the factory did.
You can download the owner's manual with parts list from the Atlas-Craftsman section in our DOWNLOADS. Instructions for navigating DOWNLOADS are a few threads below where you posted the above. And if you didn't get a copy of the Atlas Manual Of Lathe Operation (MOLO for short) with the machine, you need one. They turn up on eBay fairly frequently, usually at around $35 +/-. The best edition for your machine is the 16th, printed in 1954 and 1955. And preferably one that says CRAFTSMAN on the black front cover. If you watch eBay for a while, one will turn up. Unfortunately, the only extra 16th edition that I have is the one optimised for the Atlas 10".
The proper size QCTP for the Craftsman 12" is an AXA. There are people on here and elsewhere who have put a BXA on their Atlas built 12". But they fall into two groups - those who say that they wished that they hadn't, and those that wish it but don't admit it. Unless you are rich enough or lucky enough to buy an Aloris, what you buy will probably be made in China these days. So I would pay a few dollars more and get the wedge type. Don't buy the cheapest one that you can find. And don't buy one with an aluminum tool post. Whatever you buy, you will probably have to machine the T-nut to fit the T-slot on your compound slide. You can do this on the lathe if you got it with a lantern tool post. But I wouldn't do that because you will have to cut away too much of the nut and you will increase the risk of breaking the top of the compound.
Most of the QCTP's can be had as a package deal with one each of four or five different cutter holders. Buy several additional #101 holders (I currently have 12) and probably two additional #102 holders. If you don't, every time that you need to use a different cutter, you lose most the benefits of a QCTP because you have to stop, get out the Allen wrench, remove the cutter that you were using, install the new one, and get it on center.