I'd check the timing before you put it all back together because if that is the case you run a high risk of wrecking all the new parts on the first startup. All you need to do is make sure it's on the right click, since it's an older engine it should have a dual chain system instead of a belt which is easier to set. Sounds to me like you have a warped flywheel, or the bellhousing is too large and it's causing the starter to be short of the flywheel and not being able to make a good, solid connection between the 2.
If the timing does end up being the cause, you may want to figure out what sent it off in the first place. Could be something as simple as stretched steel if it runs a dual chain. Like I said, I'm pretty confident this is the cause, simply because I've seen 383's bolt up to T5's no problem in person, without any kind of adapters.
If you end up having a warped flywheel, since all the teeth aren't meshing together and it starts after a few cranks, all you may have to do is replace it with the one it already has. It only takes a few degrees to mess eveything up on that too.
And if that is the case you may want to figure out how that happen. Could have been from a misfire....and that goes back to bad timing. Misfires can be difficult to detect at times.