I haven't done a lot of dog turning but I actually find most of them to be kind of hit & miss. Either the return arm is too short as you are experiencing. Or it covers up so much of the shaft. The retention basically boils down to cinching that bolt in the vee notch so unless you are also going to mill a flat on the part, I don't get why the whole arm has to be so massive. Also dog plates are getting harder to find.
I've drawn up a CAD design for a dog that is made from simple plate say 1/2" thick. Progressively larger series of plates so like 0-.5" stock, 0.5-1.0" etc. Then its arm holds a pin of any length that can rest in the dog plate or chuck jaw or faceplate. I'm told faceplates aren't really meant for transmitting torque like this though. I'll dig up the design if you are interested. The trick is making the teardrop internal shape. I also had a thought to make a dog plate from a ordinary chuck adapter plate, D1-4 in my case.
Anyways one thing to remember, if you are threading using the dog, always ensure pre-contact with the pin & chuck before in-feeding so threads don't get out of phase.