My experience buying Detroit parts:
This little stunt required a new side gear, new clutch/HOR assembly, and new spring retainer.
Someone recommended I talk to Jack @ CTM, and he went out of his way to check with some of his personal contacts to see if anyone had them on a shelf somewhere. Called me back the next day with bad news, seemed that no one had them and I was looking at 6+ weeks until the next production run.
I also contacted a guy in PA who runs a small 4x4 shop who had helped me out in the past. I gave him the part numbers I was looking for, he got back to me two days later. He ended up finding me a side gear in Michigan, and the clutch/HOR and spring retainer in Tennessee. I had them all 3 days later, all brand new parts.
Side gear was $140, clutch was $150, retainer was $12. Mine was a Dana 60, but I wouldn't expect Dana 44 parts to be much less, if at all.
In looking through my Detroit parts catalog I can't find any listings for 33-spline D44 gears, and it looks like it may have been a part special to the Superior Super 44 kit (they designed the Detroit specially for that kit). It may be worth your time to talk to the guy who found my parts for me though...his name is Barry @ Truck Stuff and More, 814-357-8142.