How to avoid cramped/compressed breathing?
I see you are aware of horizontal breathing vs vertical breathing - the former is "belly breathing" as you name it, the latter is the shallow type with shoulders vertical movement involved (hence less effective).

Perhaps this helps: on my firefighter training we've learned how to cope with hyperventilation - make sure you exhale deeply. The body will take care for inhale itself provided the lungs are properly emptied.

Good luck!