I don't think any Cuban I've had has pulled pork, usually it's sliced pernil, not shredded. Now, usually it's so tender the slices break into chunks. Maybe that's NY Cubans but I do like it this way. I don't want it shredded like BBQ pulled pork.
No salami and no shreds either ... you are on-point in my book ...
I had a very nice version at the Don Shula down in MIA where they use a pretzel roll and cure 81 ham ... was killer.