I keep looking for a D1-4 drive plate but they are less common, might be just as easy to make it from a cheapo chuck adapter plate.
I generally buy D1-5 backplates for all my custom chucks. Accusize has them in cast iron and steel. The steel ones are thicker and stronger. I bet I have 4 of the cast iron ones and two of the steel from Accusize and two old ones from Grizzly.
IF I was going to do what you are doing that's what I would do again.
Frankly, I don't see any advantage to this method. I can chuck a short piece of big bar in my 3 jaw and make a better center than one can buy with zero worries about fit cuz it is made on the chuck and spindle it will be used with. Any runout of any part (except bearings) is automatically eliminated because the 60 degree center taper is machined in place. The really nice thing about using a 3 jaw this way is that it inherently provides a great driving location for the drive dog.