Dual point distributor question

I’m getting very close to being able to fire up my 67 barracuda for the first time since I bought it. I pulled the 273 commando engine and had it machined, rebuilt the heads, etc and I’ve now got everything installed and I’m ready to break in the cam and lifters since I had them ground.
Anyways, I had a dual points distributor and I was testing for spark at the points yesterday to make sure everything is good to go, and I noticed a lot of play in the distributor shaft; so much so that if I open the one set of points by lightly twisting a flat blade screw driver against the cam, the shaft moves over the opposite way and will partially move the other set of points, even though the shaft didn’t rotate at all which I’m guessing will lead to a nightmare of setting the dwell etc and getting the 2 sets perfectly set up.

My question is, can I get a bushing set and rebuild the thing, or do I need to send it out?