Unless you can grind every tool bit to be exactly the same height as the top of the shank the cutting tip will be below centerline. That is why the slot for the tool bit has to be bigger than 1/2" with a portion above centerline and the rest below centerline. Make it at least 9/16. 5/8 would be better. That way you have room to shim the tool bit so the the tip of the tool bit is on centerline. The actual size of the slot is not critical.
To eliminate having to fiddle with shims every time you change a tool bit you can glue the shims to be bottom of the shank. A poor man's QCTP. Maybe we should call it a quick change tool bit. QCTB.
You can use an end mill in the chuck to cut the slot. You just need to shim the 4 way to get the slot at the proper height. Hog out most of the slot with a drill and do the final cut to size on the lathe.
Another thought. You could make a Norman style QCTP in the same amount of time as making a 4 way. I was researching how to make a 4 way when I stumbled on to making a Norman style QCTP. Here is my thread on the Norman.
https://www.hobby-machinist.com/threads/norman-style-qctp.79705/