I am glad to see that the rate drops to normal range (20-30 beats per minute) at rest. That along with those pink gums (a sign of good oxygenation) allows us to put issues that would actually compromise his breathing (ie allergic lung disease, pneumonia, etc) lower on his list of concerns. As well, his signs would make heart disease less of a concern here as well.
Instead, if we are hearing breathing changes and coughing with excitement, then I'd be concerned that we could have an issue in the upper airway itself. Common causes include laryngeal paralysis (where the sounds, increased rate, and coughing are related to the laryngeal flaps not pulling back to dilate the airway as they are supposed to) or tracheal collapse (where the neck muscles pull the trachea taut such that it collapses on itself and they cough to try to reopen the trachea). Otherwise, we could also be seeing these signs with a low grade bronchitis or asthma.
In this situation, its good that his vet has recognized that we do have an issue here that we need to look into. Still, if they haven't diagnosed it, then we'd be best to follow up with them. Just to give them a clear idea of what he is doing when he have these episodes (since dogs don't always show us what they are up to during their visits), it would be ideal to video one of these episodes. Based on what they see and their assessment of the airway, heart, and lungs (+/- an xray) we can pinpoint which issue is present. And if the signs are intermittent, then he may just need medical management (ie anti-inflammatories, bronchodilators, etc) or if laryngeal paralysis is confirmed the surgery could be curative for him.
Overall, we do have a few concerns with the signs you have reported and will want his vet to look into this properly for him. That way we can pinpoint which one is present and at least start symptomatic care to ease his signs and keep him breathing comfortably for us.
Please take care,