Ok, a picture's worth at least a few words, right? A saving grace of this machine is that it did come with a full set of exploded drawings. It has helped many times to see how things come apart and where I can modify things without having unanticipated problems.
I was hoping to be able to improve the action without massive changes. Looking at the attached exploded view, I was wondering about maybe replacing the "dogs" (142, 143 - lower centre) with custom versions having a different contact face angle, and also very smooth, tough and hardened (4140 HT?). I'm definitely concerned in doing this that the clutch will have a tendency to disengage on it's own due to the pressure forcing the dogs apart. To counteract this I was thinking to add a spring or lock of some sort to the actuating lever (135) or associated parts.
Some of you have probably read posts of mine in the past dealing with this machine and its limitations. It is for this reason why I don't want to spend a ton of time on this. If I had more space, I'd almost certainly have a separate full sized lathe and mill. Who knows, maybe it just turns out to be an interesting discussion on clutches and machine design.
Regarding the angle of dog engagement, can you be more clear on whether this angle is from horizontal or vertical? Maybe a sketch or link?