Apart from any other unknown causes for cough, your history suggests that acid reflux is the dominant cause. Acid reaching the upper airways may be triggering it.
Next Steps
Avoid regular use of Bromhexine, ( increases mucus breakdown in stomach as well).
Proper small spaced out meals as much required as his health condition allows him.
Health Tips
A gap of 2 hrs before a very small dinner & lying down in bed.
Raise the head end of the cot by 6 inches, should help. Rule out other medical conditions.